
Time bar (total: 7.2s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 1 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 2 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 3 |
| 75% | 18.7% | 6.2% | 75% | 0% | 0% | 0% | 4 |
| 87.5% | 21.8% | 3.1% | 75% | 0% | 0% | 0% | 5 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 6 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 7 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 8 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 9 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 10 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 11 |
| 99.2% | 24.8% | 0.2% | 75% | 0% | 0% | 0% | 12 |
Compiled 19 to 14 computations (26.3% saved)
| 1.0s | 8 256× | 0 | valid |
ival-sin: 255.0ms (31.7% of total)ival-cos: 226.0ms (28.1% of total)ival-mult: 138.0ms (17.2% of total)ival-<=: 63.0ms (7.8% of total)ival-div: 54.0ms (6.7% of total)ival-add: 42.0ms (5.2% of total)ival-and: 11.0ms (1.4% of total)exact: 11.0ms (1.4% of total)ival-assert: 3.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | e |
| 0 | 0 | - | 0 | - | (*.f64 e (cos.f64 v)) |
| 0 | 0 | - | 0 | - | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 0 | 0 | - | 0 | - | v |
| 0 | 0 | - | 0 | - | (sin.f64 v) |
| 0 | 0 | - | 0 | - | (*.f64 e (sin.f64 v)) |
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) |
| 0 | 0 | - | 0 | - | (cos.f64 v) |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 62.0ms | 510× | 0 | valid |
| 0.0ms | 2× | 1 | valid |
Compiled 79 to 31 computations (60.8% saved)
ival-cos: 12.0ms (32.7% of total)ival-sin: 11.0ms (30% of total)ival-mult: 7.0ms (19.1% of total)ival-div: 3.0ms (8.2% of total)ival-add: 2.0ms (5.5% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 524× | times-frac |
| 318× | distribute-lft-neg-in |
| 308× | distribute-rgt-in |
| 302× | associate-*r* |
| 292× | associate-*l* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 63 |
| 1 | 64 | 57 |
| 2 | 152 | 55 |
| 3 | 402 | 55 |
| 4 | 1000 | 55 |
| 5 | 1548 | 55 |
| 6 | 1723 | 55 |
| 7 | 1874 | 55 |
| 8 | 2030 | 55 |
| 9 | 2445 | 55 |
| 10 | 2540 | 55 |
| 11 | 2601 | 55 |
| 12 | 2653 | 55 |
| 13 | 2658 | 55 |
| 0 | 9 | 11 |
| 0 | 15 | 11 |
| 1 | 22 | 11 |
| 2 | 25 | 11 |
| 3 | 26 | 11 |
| 0 | 26 | 10 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| Outputs |
|---|
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
(*.f64 (/.f64 e (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (sin.f64 v)) |
(negabs v)
Compiled 11 to 9 computations (18.2% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.7% | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 11 to 9 computations (18.2% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (*.f64 e (sin.f64 v)) | |
| cost-diff | 0 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) | |
| cost-diff | 128 | (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) |
| 16× | lower-*.f32 |
| 12× | lower-*.f64 |
| 8× | *-commutative |
| 6× | lower-/.f32 |
| 4× | associate-/l* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 32 |
| 0 | 15 | 32 |
| 1 | 22 | 32 |
| 2 | 25 | 32 |
| 3 | 26 | 32 |
| 0 | 26 | 30 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
(*.f64 e (sin.f64 v)) |
e |
(sin.f64 v) |
v |
(+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) |
#s(literal 1 binary64) |
(*.f64 e (cos.f64 v)) |
(cos.f64 v) |
| Outputs |
|---|
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
(*.f64 (/.f64 e (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (sin.f64 v)) |
(*.f64 e (sin.f64 v)) |
(*.f64 (sin.f64 v) e) |
e |
(sin.f64 v) |
v |
(+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 e (cos.f64 v)) |
(*.f64 (cos.f64 v) e) |
(cos.f64 v) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) | |
| accuracy | 0.04296875 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) | |
| accuracy | 0.125 | (*.f64 e (cos.f64 v)) | |
| accuracy | 0.15234375 | (*.f64 e (sin.f64 v)) |
| 25.0ms | 255× | 0 | valid |
| 0.0ms | 1× | 1 | valid |
Compiled 34 to 11 computations (67.6% saved)
ival-sin: 6.0ms (34.8% of total)ival-cos: 5.0ms (29% of total)ival-mult: 3.0ms (17.4% of total)ival-div: 1.0ms (5.8% of total)ival-add: 1.0ms (5.8% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ()) |
#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ()) |
#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ()) |
#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (+ 1 e) (taylor 0 v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* -1/2 (* e (pow v 2))))) (taylor 0 v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) (taylor 0 v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) (taylor 0 v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ e (* -1/6 (* e (pow v 2))))) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt v (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* -1/6 (pow v 2)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt e (taylor 0 v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (+ e (* -1/2 (* e (pow v 2)))) (taylor 0 v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2)))))) (taylor 0 v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e)))))) (taylor 0 v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor -inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor -inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor -inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor -inf v) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor -inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor -inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor -inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e (sin v)) (+ 1 (* e (cos v)))) (taylor -inf v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor -inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor -inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor -inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (sin v) (taylor -inf v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf v) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor 0 e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor 0 e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* e (cos v))) (taylor 0 e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor 0 e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) (taylor 0 e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) (taylor 0 e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) (taylor 0 e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor 0 e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor 0 e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor 0 e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor 0 e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor 0 e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor 0 e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor 0 e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor 0 e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (cos v) (/ 1 e))) (taylor inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (cos v) (/ 1 e))) (taylor inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* e (+ (cos v) (/ 1 e))) (taylor inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin v) (cos v)) (taylor inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) (taylor inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) (taylor inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) (taylor inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) (taylor -inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) (taylor -inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) (taylor -inf e) (#s(alt (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) (patch (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (sin v) (cos v)) (taylor -inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) (taylor -inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) (taylor -inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) (taylor -inf e) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) (patch (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (sin v)) (taylor -inf e) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* e (cos v)) (taylor -inf e) (#s(alt (*.f64 e (cos.f64 v)) (patch (*.f64 e (cos.f64 v)) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | v | @ | inf | ((+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (sin v) (* e (cos v))) |
| 3.0ms | v | @ | -inf | ((+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (sin v) (* e (cos v))) |
| 2.0ms | e | @ | 0 | ((+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (sin v) (* e (cos v))) |
| 2.0ms | v | @ | 0 | ((+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (sin v) (* e (cos v))) |
| 2.0ms | e | @ | inf | ((+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (sin v) (* e (cos v))) |
| 1× | egg-herbie |
| 15 582× | lower-fma.f64 |
| 15 582× | lower-fma.f32 |
| 6 122× | lower-*.f64 |
| 6 122× | lower-*.f32 |
| 3 736× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 182 | 1153 |
| 1 | 554 | 1138 |
| 2 | 1582 | 1106 |
| 3 | 5266 | 1024 |
| 0 | 8387 | 956 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ 1 e) |
(+ 1 (+ e (* -1/2 (* e (pow v 2))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* e v) |
(* v (+ e (* -1/6 (* e (pow v 2))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
e |
(+ e (* -1/2 (* e (pow v 2)))) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2)))))) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e)))))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
1 |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
| Outputs |
|---|
(+ 1 e) |
(+.f64 e #s(literal 1 binary64)) |
(+ 1 (+ e (* -1/2 (* e (pow v 2))))) |
(fma.f64 (fma.f64 (*.f64 v v) #s(literal -1/2 binary64) #s(literal 1 binary64)) e #s(literal 1 binary64)) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) |
(fma.f64 (*.f64 e (fma.f64 #s(literal 1/24 binary64) (*.f64 v v) #s(literal -1/2 binary64))) (*.f64 v v) (+.f64 e #s(literal 1 binary64))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) |
(fma.f64 (*.f64 e (fma.f64 #s(literal -1/720 binary64) (pow.f64 v #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 v v) #s(literal -1/2 binary64)))) (*.f64 v v) (+.f64 e #s(literal 1 binary64))) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 #s(literal -1/24 binary64) e) (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64))))) (*.f64 v v) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 v v) (/.f64 e (+.f64 e #s(literal 1 binary64)))) v) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 #s(literal -1/24 binary64) e) (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64))))) #s(literal -1/5040 binary64)) (neg.f64 (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64)))))))) (*.f64 v v) (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) #s(literal 1/120 binary64)) (*.f64 (*.f64 #s(literal -1/24 binary64) e) (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))))) (*.f64 v v) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 v v) (/.f64 e (+.f64 e #s(literal 1 binary64)))) v) |
(* e v) |
(*.f64 v e) |
(* v (+ e (* -1/6 (* e (pow v 2))))) |
(*.f64 e (fma.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/6 binary64) v)) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) |
(*.f64 (*.f64 e (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) (*.f64 v v) #s(literal 1 binary64))) v) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 e (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 v v) #s(literal 1/120 binary64)) (*.f64 v v) #s(literal -1/6 binary64))) (*.f64 v e)) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/6 binary64) v) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) v) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 v v) #s(literal 1/120 binary64)) (*.f64 v v) #s(literal -1/6 binary64)) v) |
e |
(+ e (* -1/2 (* e (pow v 2)))) |
(fma.f64 (*.f64 (*.f64 v v) e) #s(literal -1/2 binary64) e) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2)))))) |
(fma.f64 (*.f64 e (fma.f64 #s(literal 1/24 binary64) (*.f64 v v) #s(literal -1/2 binary64))) (*.f64 v v) e) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e)))))) |
(fma.f64 (*.f64 e (fma.f64 #s(literal -1/720 binary64) (pow.f64 v #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (*.f64 v v) #s(literal -1/2 binary64)))) (*.f64 v v) e) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(sin v) |
(sin.f64 v) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
1 |
#s(literal 1 binary64) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(+ 1 (* e (cos v))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(*.f64 (*.f64 (sin.f64 v) (fma.f64 (*.f64 (cos.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) e #s(literal 1 binary64))) e) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(*.f64 (fma.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) e (cos.f64 v))) (sin.f64 v)) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (+ (cos v) (/ 1 e))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* e (+ (cos v) (/ 1 e))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* e (+ (cos v) (/ 1 e))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) #s(literal 1 binary64)) (/.f64 (sin.f64 v) (cos.f64 v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) #s(literal 1 binary64)) (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) e)) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) #s(literal 1 binary64)) (/.f64 (sin.f64 v) (cos.f64 v)) (*.f64 (/.f64 (/.f64 (sin.f64 v) e) e) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 4 binary64)) e)) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))))) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) #s(literal 1 binary64)) (/.f64 (sin.f64 v) (cos.f64 v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) #s(literal 1 binary64)) (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
| 5 798× | lower-fma.f64 |
| 5 798× | lower-fma.f32 |
| 4 350× | lower-/.f32 |
| 4 348× | lower-/.f64 |
| 3 988× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 27 |
| 0 | 15 | 27 |
| 1 | 42 | 27 |
| 2 | 241 | 27 |
| 3 | 2097 | 27 |
| 0 | 8370 | 25 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v))) |
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
(*.f64 e (sin.f64 v)) |
(sin.f64 v) |
(*.f64 e (cos.f64 v)) |
| Outputs |
|---|
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Compiled 12 121 to 1 266 computations (89.6% saved)
12 alts after pruning (12 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 438 | 12 | 450 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 439 | 12 | 451 |
| Status | Accuracy | Program |
|---|---|---|
| 72.0% | (pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| 22.9% | (/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (neg.f64 e) (sin.f64 v)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 v) e) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 (neg.f64 e) (sin.f64 v)))))) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) | |
| ▶ | 98.7% | (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
| 99.6% | (/.f64 e (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (sin.f64 v))) | |
| 99.0% | (/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) (*.f64 (sin.f64 v) e))) | |
| ▶ | 99.7% | (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
| 99.7% | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) | |
| 50.4% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v))) | |
| ▶ | 99.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
| ▶ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
| ▶ | 50.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
| 96.8% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
Compiled 338 to 252 computations (25.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) | |
| cost-diff | 0 | (neg.f64 e) | |
| cost-diff | 0 | (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) | |
| cost-diff | 0 | #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (*.f64 e (sin.f64 v)) | |
| cost-diff | 0 | (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| cost-diff | 0 | (+.f64 e #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 e (+.f64 e #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (*.f64 (sin.f64 v) e) | |
| cost-diff | 0 | (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) | |
| cost-diff | 13696 | (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
| 13 376× | lower-fma.f32 |
| 13 372× | lower-fma.f64 |
| 4 112× | lower-*.f32 |
| 4 100× | lower-*.f64 |
| 3 514× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 241 |
| 0 | 56 | 241 |
| 1 | 98 | 241 |
| 2 | 202 | 241 |
| 3 | 445 | 233 |
| 4 | 1145 | 233 |
| 5 | 3847 | 233 |
| 0 | 8544 | 227 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sin.f64 v) e) |
(sin.f64 v) |
v |
e |
(-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) |
(*.f64 (cos.f64 v) e) |
(cos.f64 v) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(fma.f64 (cos.f64 v) e #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/.f64 e (+.f64 e #s(literal 1 binary64))) |
e |
(+.f64 e #s(literal 1 binary64)) |
#s(literal 1 binary64) |
v |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(*.f64 e (sin.f64 v)) |
e |
(sin.f64 v) |
v |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
(+.f64 e #s(literal 1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
(*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) |
(fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) |
(neg.f64 e) |
e |
(cos.f64 v) |
v |
#s(literal 1 binary64) |
(*.f64 (sin.f64 v) e) |
(sin.f64 v) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(sin.f64 v) |
v |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(cos.f64 v) |
(/.f64 #s(literal -1 binary64) e) |
#s(literal -1 binary64) |
e |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(*.f64 (/.f64 e (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (sin.f64 v)) |
(/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (/.f64 e (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (sin.f64 v)) |
(*.f64 (sin.f64 v) e) |
(*.f64 e (sin.f64 v)) |
(sin.f64 v) |
v |
e |
(-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) |
(*.f64 (cos.f64 v) e) |
(cos.f64 v) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(fma.f64 (cos.f64 v) e #s(literal -1 binary64)) |
#s(literal -1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (-.f64 e #s(literal -1 binary64))) v)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(*.f64 (/.f64 e (-.f64 e #s(literal -1 binary64))) v) |
(/.f64 e (+.f64 e #s(literal 1 binary64))) |
(/.f64 e (-.f64 e #s(literal -1 binary64))) |
e |
(+.f64 e #s(literal 1 binary64)) |
(-.f64 e #s(literal -1 binary64)) |
#s(literal 1 binary64) |
v |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64)))) |
(*.f64 e (sin.f64 v)) |
e |
(sin.f64 v) |
v |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
#s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64))) |
(+.f64 e #s(literal 1 binary64)) |
(-.f64 e #s(literal -1 binary64)) |
#s(literal 1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e) (sin.f64 v))) |
(*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) |
(*.f64 (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e) (sin.f64 v)) |
(fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) |
(neg.f64 e) |
e |
(cos.f64 v) |
v |
#s(literal 1 binary64) |
(*.f64 (sin.f64 v) e) |
(*.f64 e (sin.f64 v)) |
(sin.f64 v) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(sin.f64 v) |
v |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(cos.f64 v) |
(/.f64 #s(literal -1 binary64) e) |
#s(literal -1 binary64) |
e |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (cos.f64 v) | |
| accuracy | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) | |
| accuracy | 0.0078125 | (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) | |
| accuracy | 0.29296875 | (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) | |
| accuracy | 0 | (cos.f64 v) | |
| accuracy | 0.0234375 | (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) | |
| accuracy | 0.15234375 | (*.f64 (sin.f64 v) e) | |
| accuracy | 0.948985689689801 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) | |
| accuracy | 0 | (sin.f64 v) | |
| accuracy | 0.04296875 | (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| accuracy | 0.15234375 | (*.f64 e (sin.f64 v)) | |
| accuracy | 0.674999020658834 | #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) | |
| accuracy | 0 | (+.f64 e #s(literal 1 binary64)) | |
| accuracy | 0.01953125 | (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) | |
| accuracy | 0.02734375 | (/.f64 e (+.f64 e #s(literal 1 binary64))) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) | |
| accuracy | 0.03125 | (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) | |
| accuracy | 0.125 | (*.f64 (cos.f64 v) e) | |
| accuracy | 0.15234375 | (*.f64 (sin.f64 v) e) | |
| accuracy | 0.154628759768442 | (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) |
| 125.0ms | 255× | 0 | valid |
| 0.0ms | 1× | 1 | valid |
Compiled 209 to 30 computations (85.6% saved)
ival-mult: 43.0ms (55.6% of total)ival-div: 8.0ms (10.3% of total)ival-add: 7.0ms (9.1% of total)ival-sin: 7.0ms (9.1% of total)ival-cos: 7.0ms (9.1% of total)ival-sub: 2.0ms (2.6% of total)ival-pow2: 2.0ms (2.6% of total)ival-neg: 1.0ms (1.3% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (patch (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (sin.f64 v) e) (patch (*.f64 (sin.f64 v) e) #<representation binary64>) () ()) |
#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) (patch (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) #<representation binary64>) () ()) |
#s(alt (/.f64 e (+.f64 e #s(literal 1 binary64))) (patch (/.f64 e (+.f64 e #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 e #s(literal 1 binary64)) (patch (+.f64 e #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) (patch (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) (patch #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) (patch (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (patch (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) (patch (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ()) |
#s(alt (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) (patch (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ()) |
#s(alt (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) (patch (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (cos.f64 v) e) (patch (*.f64 (cos.f64 v) e) #<representation binary64>) () ()) |
#s(alt (cos.f64 v) (patch (cos.f64 v) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (* e (* v (- e 1))) (- (pow e 2) 1)) (taylor 0 v) (#s(alt (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) (taylor 0 v) (#s(alt (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (/ (* e v) (- (pow e 2) 1)) (taylor 0 v) (#s(alt (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (patch (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 (sin.f64 v) e) (patch (*.f64 (sin.f64 v) e) #<representation binary64>) () ())) ()) |
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#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) (taylor 0 v) (#s(alt (*.f64 (sin.f64 v) e) (patch (*.f64 (sin.f64 v) e) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) (taylor 0 v) (#s(alt (*.f64 (sin.f64 v) e) (patch (*.f64 (sin.f64 v) e) #<representation binary64>) () ())) ()) |
#s(alt v (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* -1/6 (pow v 2)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
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#s(alt (* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
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#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) (patch (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) (patch (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) (patch (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) (patch (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) (patch (/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
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#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) (taylor 0 v) (#s(alt (*.f64 e (sin.f64 v)) (patch (*.f64 e (sin.f64 v)) #<representation binary64>) () ())) ()) |
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | v | @ | 0 | ((* (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (+ (* (cos v) e) -1)) (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (* (sin v) e) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (/ e (+ e 1)) (+ e 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (+ (* (neg e) (cos v)) 1) (neg e) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (sin v) (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (pow (* (cos v) e) 2) (* (cos v) e) (cos v)) |
| 8.0ms | v | @ | inf | ((* (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (+ (* (cos v) e) -1)) (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (* (sin v) e) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (/ e (+ e 1)) (+ e 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (+ (* (neg e) (cos v)) 1) (neg e) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (sin v) (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (pow (* (cos v) e) 2) (* (cos v) e) (cos v)) |
| 7.0ms | e | @ | inf | ((* (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (+ (* (cos v) e) -1)) (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (* (sin v) e) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (/ e (+ e 1)) (+ e 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (+ (* (neg e) (cos v)) 1) (neg e) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (sin v) (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (pow (* (cos v) e) 2) (* (cos v) e) (cos v)) |
| 5.0ms | v | @ | -inf | ((* (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (+ (* (cos v) e) -1)) (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (* (sin v) e) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (/ e (+ e 1)) (+ e 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (+ (* (neg e) (cos v)) 1) (neg e) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (sin v) (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (pow (* (cos v) e) 2) (* (cos v) e) (cos v)) |
| 4.0ms | e | @ | -inf | ((* (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (+ (* (cos v) e) -1)) (/ (* (sin v) e) (- (pow (* (cos v) e) 2) 1)) (* (sin v) e) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (/ e (+ e 1)) (+ e 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ 1 (* e (cos v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (+ (* (neg e) (cos v)) 1) (neg e) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (sin v) (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (pow (* (cos v) e) 2) (* (cos v) e) (cos v)) |
| 1× | egg-herbie |
| 14 148× | lower-fma.f64 |
| 14 148× | lower-fma.f32 |
| 6 682× | lower-*.f64 |
| 6 682× | lower-*.f32 |
| 4 016× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 583 | 7025 |
| 1 | 1899 | 6814 |
| 2 | 5718 | 6703 |
| 0 | 8332 | 6334 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (* e (* v (- e 1))) (- (pow e 2) 1)) |
(* v (+ (* (pow v 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
(* v (+ (* (pow v 2) (- (+ (* (pow v 2) (- (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1))) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
(* v (+ (* (pow v 2) (- (+ (* (pow v 2) (- (+ (* (pow v 2) (- (/ (* e (+ (* -1/144 e) (+ (* -1/240 e) (+ (* -1/720 e) (* -1/5040 (- e 1)))))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (- (pow e 2) 1))) (+ (* -2/45 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))) (* 1/3 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))))))) (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1))) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1))) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
(/ (* e v) (- (pow e 2) 1)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (- (pow e 2) 1))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (/ e (- (pow e 2) 1)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (- (pow e 2) 1))) (* (pow v 2) (- (* 1/120 (/ e (- (pow e 2) 1))) (+ (* -1 (/ (* (pow e 2) (- (* -1/6 (/ e (- (pow e 2) 1))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (/ e (- (pow e 2) 1)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (- (pow e 2) 1))) (* (pow v 2) (- (+ (* 1/120 (/ e (- (pow e 2) 1))) (* (pow v 2) (- (* -1/5040 (/ e (- (pow e 2) 1))) (+ (* -1 (/ (* (pow e 2) (- (* 1/120 (/ e (- (pow e 2) 1))) (+ (* -1 (/ (* (pow e 2) (- (* -1/6 (/ e (- (pow e 2) 1))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (pow e 3) (pow (- (pow e 2) 1) 2)))))) (- (pow e 2) 1))) (+ (* -2/45 (/ (pow e 3) (pow (- (pow e 2) 1) 2))) (* 1/3 (/ (* (pow e 2) (- (* -1/6 (/ e (- (pow e 2) 1))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1)))))))) (+ (* -1 (/ (* (pow e 2) (- (* -1/6 (/ e (- (pow e 2) 1))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))))) (* -1 (/ (pow e 3) (pow (- (pow e 2) 1) 2))))) (/ e (- (pow e 2) 1)))) |
(* e v) |
(* v (+ e (* -1/6 (* e (pow v 2))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* e v) |
(* v (+ e (* -1/6 (* e (pow v 2))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) |
(+ 1 e) |
(+ 1 (+ e (* -1/2 (* e (pow v 2))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* e (* v (+ 1 (* -1 e)))) |
(* v (+ (* e (* (pow v 2) (+ (* -1/6 (+ 1 (* -1 e))) (* 1/2 e)))) (* e (+ 1 (* -1 e))))) |
(* v (+ (* e (+ 1 (* -1 e))) (* (pow v 2) (+ (* e (* (pow v 2) (+ (* -1/12 e) (+ (* -1/24 e) (* 1/120 (+ 1 (* -1 e))))))) (* e (+ (* -1/6 (+ 1 (* -1 e))) (* 1/2 e))))))) |
(* v (+ (* e (+ 1 (* -1 e))) (* (pow v 2) (+ (* e (+ (* -1/6 (+ 1 (* -1 e))) (* 1/2 e))) (* (pow v 2) (+ (* e (* (pow v 2) (+ (* -1/5040 (+ 1 (* -1 e))) (+ (* 1/720 e) (+ (* 1/240 e) (* 1/144 e)))))) (* e (+ (* -1/12 e) (+ (* -1/24 e) (* 1/120 (+ 1 (* -1 e)))))))))))) |
(+ 1 (* -1 e)) |
(+ 1 (+ (* -1 e) (* 1/2 (* e (pow v 2))))) |
(+ 1 (+ (* -1 e) (* (pow v 2) (+ (* -1/24 (* e (pow v 2))) (* 1/2 e))))) |
(+ 1 (+ (* -1 e) (* (pow v 2) (+ (* 1/2 e) (* (pow v 2) (+ (* -1/24 e) (* 1/720 (* e (pow v 2))))))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ v (+ 1 (/ 1 e))) |
(* v (+ (* (pow v 2) (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (+ (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (* (pow v 2) (- (* 1/720 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (+ (* -1/2 (/ (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))) (+ 1 (/ 1 e)))) (+ (* 1/5040 (/ 1 (+ 1 (/ 1 e)))) (* 1/24 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e))))))))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(+ 1 (/ 1 e)) |
(+ 1 (+ (* -1/2 (pow v 2)) (/ 1 e))) |
(+ 1 (+ (* (pow v 2) (- (* 1/24 (pow v 2)) 1/2)) (/ 1 e))) |
(+ 1 (+ (* (pow v 2) (- (* (pow v 2) (+ 1/24 (* -1/720 (pow v 2)))) 1/2)) (/ 1 e))) |
(pow e 2) |
(+ (* -1 (* (pow e 2) (pow v 2))) (pow e 2)) |
(+ (* (pow v 2) (+ (* -1 (pow e 2)) (* 1/3 (* (pow e 2) (pow v 2))))) (pow e 2)) |
(+ (* (pow v 2) (+ (* -1 (pow e 2)) (* (pow v 2) (+ (* -2/45 (* (pow e 2) (pow v 2))) (* 1/3 (pow e 2)))))) (pow e 2)) |
e |
(+ e (* -1/2 (* e (pow v 2)))) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2)))))) |
(+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e)))))) |
1 |
(+ 1 (* -1/2 (pow v 2))) |
(+ 1 (* (pow v 2) (- (* 1/24 (pow v 2)) 1/2))) |
(+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/24 (* -1/720 (pow v 2)))) 1/2))) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(cos v) |
(cos v) |
(cos v) |
(cos v) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (* (sin v) (- (* e (cos v)) 1))) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(/ (* e (sin v)) (- (* (pow e 2) (pow (cos v) 2)) 1)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(* e (* (sin v) (+ 1 (* -1 (* e (cos v)))))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(/ (sin v) (+ (cos v) (/ 1 e))) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(cos v) |
(cos v) |
(cos v) |
(cos v) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (+ (* -1 (* (cos v) (sin v))) (* e (* (pow (cos v) 2) (sin v))))))) |
(* e (+ (sin v) (* e (+ (* -1 (* (cos v) (sin v))) (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))))))) |
(* -1 (* e (sin v))) |
(* e (+ (* -1 (sin v)) (* -1 (* (pow e 2) (* (pow (cos v) 2) (sin v)))))) |
(* e (+ (* -1 (sin v)) (* (pow e 2) (- (* -1 (* (pow e 2) (* (pow (cos v) 4) (sin v)))) (* (pow (cos v) 2) (sin v)))))) |
(* e (+ (* -1 (sin v)) (* (pow e 2) (- (* (pow e 2) (- (* -1 (* (pow e 2) (* (pow (cos v) 6) (sin v)))) (* (pow (cos v) 4) (sin v)))) (* (pow (cos v) 2) (sin v)))))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e v) |
(* e (+ v (* -1 (* e v)))) |
(* e (+ v (* e (- (* e v) v)))) |
(* e (+ v (* e (- (* e (- (* -1 (* e v)) (* -1 v))) v)))) |
e |
(* e (+ 1 (* -1 e))) |
(* e (+ 1 (* e (- e 1)))) |
(* e (+ 1 (* e (- (* e (+ 1 (* -1 e))) 1)))) |
1 |
(+ 1 e) |
(+ 1 e) |
(+ 1 e) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
1 |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
1 |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(+ 1 (* -1 (* e (cos v)))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(/ 1 e) |
(/ (+ 1 (* e (cos v))) e) |
(/ (+ 1 (* e (cos v))) e) |
(/ (+ 1 (* e (cos v))) e) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3))))) |
(- (+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v)))) (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3))))) |
(/ (sin v) (* e (pow (cos v) 2))) |
(/ (+ (/ (sin v) (* (pow e 2) (pow (cos v) 4))) (/ (sin v) (pow (cos v) 2))) e) |
(/ (- (+ (/ (sin v) (* (pow e 4) (pow (cos v) 6))) (/ (sin v) (pow (cos v) 2))) (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 4))))) e) |
(/ (- (+ (/ (sin v) (* (pow e 6) (pow (cos v) 8))) (/ (sin v) (pow (cos v) 2))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 4)))) (* -1 (/ (sin v) (* (pow e 4) (pow (cos v) 6)))))) e) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
v |
(+ v (* -1 (/ v e))) |
(- (+ v (/ v (pow e 2))) (/ v e)) |
(- (+ v (* -1 (/ v (pow e 3)))) (+ (* -1 (/ v (pow e 2))) (/ v e))) |
1 |
(- 1 (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (+ (/ 1 e) (/ 1 (pow e 3)))) |
e |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (cos v)) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(* -1 (* (pow e 2) (* (cos v) (sin v)))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* -1 (* e (cos v))) |
(* e (+ (* -1 (cos v)) (/ 1 e))) |
(* e (+ (* -1 (cos v)) (/ 1 e))) |
(* e (+ (* -1 (cos v)) (/ 1 e))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(cos v) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (* e (pow (cos v) 2))) |
(* -1 (/ (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 4)))) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) |
(* -1 (/ (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 4)))) (+ (* -1 (/ (sin v) (* (pow e 4) (pow (cos v) 6)))) (* -1 (/ (sin v) (pow (cos v) 2))))) e)) |
(* -1 (/ (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 4)))) (+ (* -1 (/ (sin v) (* (pow e 4) (pow (cos v) 6)))) (+ (* -1 (/ (sin v) (* (pow e 6) (pow (cos v) 8)))) (* -1 (/ (sin v) (pow (cos v) 2)))))) e)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
v |
(+ v (* -1 (/ v e))) |
(+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) |
(+ v (* -1 (/ (+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) e))) |
1 |
(- 1 (/ 1 e)) |
(+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) |
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) e))) |
e |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (cos v)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(* -1 (* (pow e 2) (* (cos v) (sin v)))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* -1 (* e (cos v))) |
(* -1 (* e (- (cos v) (/ 1 e)))) |
(* -1 (* e (- (cos v) (/ 1 e)))) |
(* -1 (* e (- (cos v) (/ 1 e)))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (* -1 (/ (sin v) (pow (cos v) 3)))) e)) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(cos v) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* (pow e 2) (pow (cos v) 2)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
(* e (cos v)) |
| Outputs |
|---|
(/ (* e (* v (- e 1))) (- (pow e 2) 1)) |
(*.f64 (*.f64 (-.f64 e #s(literal 1 binary64)) v) (/.f64 e (fma.f64 e e #s(literal -1 binary64)))) |
(* v (+ (* (pow v 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (/.f64 e (fma.f64 e e #s(literal -1 binary64))) (/.f64 (*.f64 (pow.f64 e #s(literal 3 binary64)) (-.f64 e #s(literal 1 binary64))) (pow.f64 (fma.f64 e e #s(literal -1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (-.f64 e #s(literal 1 binary64)) v) (/.f64 e (fma.f64 e e #s(literal -1 binary64))))) |
(* v (+ (* (pow v 2) (- (+ (* (pow v 2) (- (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1))) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
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(* v (+ (* (pow v 2) (- (+ (* (pow v 2) (- (+ (* (pow v 2) (- (/ (* e (+ (* -1/144 e) (+ (* -1/240 e) (+ (* -1/720 e) (* -1/5040 (- e 1)))))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1)) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (- (pow e 2) 1))) (+ (* -2/45 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))) (* 1/3 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))))))) (/ (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))) (- (pow e 2) 1))) (+ (* -1 (/ (* (pow e 2) (- (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1)) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (- (pow e 2) 1))) (* 1/3 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2)))))) (/ (* e (+ (* -1/2 e) (* -1/6 (- e 1)))) (- (pow e 2) 1))) (* -1 (/ (* (pow e 3) (- e 1)) (pow (- (pow e 2) 1) 2))))) (/ (* e (- e 1)) (- (pow e 2) 1)))) |
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(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) |
(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (* -1 (/ (sin v) (pow (cos v) 3)))) e)) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(cos v) |
(cos.f64 v) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(* (pow e 2) (pow (cos v) 2)) |
(*.f64 (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e) e) |
(* (pow e 2) (pow (cos v) 2)) |
(*.f64 (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e) e) |
(* (pow e 2) (pow (cos v) 2)) |
(*.f64 (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e) e) |
(* (pow e 2) (pow (cos v) 2)) |
(*.f64 (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
| 6 022× | lower-fma.f32 |
| 6 018× | lower-fma.f64 |
| 4 064× | lower-/.f32 |
| 4 054× | lower-/.f64 |
| 3 820× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 191 |
| 0 | 56 | 191 |
| 1 | 221 | 191 |
| 2 | 1484 | 183 |
| 0 | 8832 | 174 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(*.f64 (sin.f64 v) e) |
(sin.f64 v) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/.f64 e (+.f64 e #s(literal 1 binary64))) |
(+.f64 e #s(literal 1 binary64)) |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(*.f64 e (sin.f64 v)) |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
(*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e)) |
(fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) |
(neg.f64 e) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) |
(*.f64 (cos.f64 v) e) |
(cos.f64 v) |
| Outputs |
|---|
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Compiled 33 724 to 3 563 computations (89.4% saved)
33 alts after pruning (30 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 441 | 26 | 1 467 |
| Fresh | 3 | 4 | 7 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1 446 | 33 | 1 479 |
| Status | Accuracy | Program |
|---|---|---|
| 72.0% | (pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| 22.9% | (/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (neg.f64 e) (sin.f64 v)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 v) e) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 (neg.f64 e) (sin.f64 v)))))) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) | |
| 50.2% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 50.4% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 98.5% | (/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) | |
| 98.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) | |
| ▶ | 99.7% | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
| 98.7% | (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) | |
| 99.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (fma.f64 (pow.f64 e #s(literal -1/2 binary64)) (pow.f64 e #s(literal -1/2 binary64)) (cos.f64 v)))) | |
| ✓ | 99.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
| 96.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) | |
| 49.9% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) | |
| 50.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) | |
| ✓ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
| ▶ | 45.4% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
| 63.8% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (sin.f64 v) (-.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) (pow.f64 e #s(literal -2 binary64)))) (-.f64 (cos.f64 v) (pow.f64 e #s(literal -1 binary64))))) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) | |
| ✓ | 50.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
| ▶ | 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
| 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 e (fma.f64 (cos.f64 v) (neg.f64 e) #s(literal 1 binary64))) (sin.f64 v))) | |
| 96.8% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) | |
| 99.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) | |
| ▶ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
| 2.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) | |
| 50.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) | |
| 97.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) | |
| 2.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) | |
| ▶ | 48.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
| 70.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)))) | |
| 49.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
Compiled 794 to 618 computations (22.2% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) | |
| cost-diff | 0 | (neg.f64 e) | |
| cost-diff | 0 | (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) | |
| cost-diff | 192 | (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) | |
| cost-diff | 2816 | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) | |
| cost-diff | 0 | (/.f64 (+.f64 #s(literal 1 binary64) e) e) | |
| cost-diff | 0 | (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) | |
| cost-diff | 704 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) | |
| cost-diff | 0 | (*.f64 v e) | |
| cost-diff | 0 | #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) | |
| cost-diff | 0 | (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
| 9 476× | lower-fma.f32 |
| 9 472× | lower-fma.f64 |
| 3 032× | lower-*.f32 |
| 3 020× | lower-*.f64 |
| 1 274× | lower-/.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 295 |
| 0 | 62 | 246 |
| 1 | 119 | 238 |
| 2 | 269 | 234 |
| 3 | 736 | 233 |
| 4 | 4137 | 233 |
| 0 | 8887 | 233 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) |
(sin.f64 v) |
v |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(cos.f64 v) |
e |
#s(literal 1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) |
(*.f64 v e) |
v |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) e) e) |
(+.f64 #s(literal 1 binary64) e) |
e |
v |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
#s(literal 0 binary64) |
(*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
(/.f64 e (-.f64 #s(literal -1 binary64) e)) |
e |
(-.f64 #s(literal -1 binary64) e) |
#s(literal -1 binary64) |
(+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
v |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
(*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) |
(neg.f64 e) |
e |
(*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(sin.f64 v) |
v |
(fma.f64 (cos.f64 v) e #s(literal -1 binary64)) |
(cos.f64 v) |
#s(literal -1 binary64) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(*.f64 (/.f64 e (fma.f64 e (cos.f64 v) #s(literal 1 binary64))) (sin.f64 v)) |
(/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) |
(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) #s(literal 1 binary64))) |
(sin.f64 v) |
v |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(fma.f64 e (cos.f64 v) #s(literal 1 binary64)) |
(cos.f64 v) |
e |
#s(literal 1 binary64) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 e v))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 e v)) |
(*.f64 v e) |
(*.f64 e v) |
v |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 v (-.f64 e #s(literal -1 binary64))) e)) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) |
(*.f64 (/.f64 v (-.f64 e #s(literal -1 binary64))) e) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) |
(/.f64 e (-.f64 e #s(literal -1 binary64))) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) e) e) |
(/.f64 (-.f64 e #s(literal -1 binary64)) e) |
(+.f64 #s(literal 1 binary64) e) |
(-.f64 e #s(literal -1 binary64)) |
e |
v |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 v (-.f64 e #s(literal -1 binary64))) e)) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v) |
(*.f64 (/.f64 v (-.f64 e #s(literal -1 binary64))) e) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
(/.f64 e (-.f64 e #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
(*.f64 (/.f64 e (-.f64 e #s(literal -1 binary64))) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
#s(literal 0 binary64) |
(*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
(/.f64 e (-.f64 #s(literal -1 binary64) e)) |
e |
(-.f64 #s(literal -1 binary64) e) |
#s(literal -1 binary64) |
(+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
(/.f64 e (-.f64 #s(literal -1 binary64) e)) |
v |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 e (sin.f64 v)))) |
(*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) |
(*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 e (sin.f64 v))) |
(neg.f64 e) |
e |
(*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(*.f64 (fma.f64 e (cos.f64 v) #s(literal -1 binary64)) (sin.f64 v)) |
(sin.f64 v) |
v |
(fma.f64 (cos.f64 v) e #s(literal -1 binary64)) |
(fma.f64 e (cos.f64 v) #s(literal -1 binary64)) |
(cos.f64 v) |
#s(literal -1 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (cos.f64 v) | |
| accuracy | 0.01953125 | (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) | |
| accuracy | 0.16796875 | (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) | |
| accuracy | 0.948985689689801 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) | |
| accuracy | 0.02734375 | (/.f64 e (-.f64 #s(literal -1 binary64) e)) | |
| accuracy | 0.0390625 | (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) | |
| accuracy | 28.520316685236192 | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| accuracy | 0.01953125 | (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) | |
| accuracy | 0.02734375 | (/.f64 (+.f64 #s(literal 1 binary64) e) e) | |
| accuracy | 0.18359375 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) | |
| accuracy | 0 | (*.f64 v e) | |
| accuracy | 1.9589692529988256 | #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) | |
| accuracy | 0 | (cos.f64 v) | |
| accuracy | 0.00390625 | (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) | |
| accuracy | 0.03515625 | (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) | |
| accuracy | 0.17578125 | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
| 69.0ms | 255× | 0 | valid |
| 0.0ms | 1× | 1 | valid |
Compiled 241 to 36 computations (85.1% saved)
ival-mult: 16.0ms (31.6% of total)ival-div: 10.0ms (19.7% of total)ival-sin: 8.0ms (15.8% of total)ival-add: 7.0ms (13.8% of total)ival-cos: 5.0ms (9.9% of total)ival-sub: 2.0ms (3.9% of total)ival-neg: 1.0ms (2% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) (patch (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) #<representation binary64>) () ()) |
#s(alt (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (patch (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ()) |
#s(alt (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (patch (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) #<representation binary64>) () ()) |
#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) (patch (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 #s(literal 1 binary64) e) e) (patch (/.f64 (+.f64 #s(literal 1 binary64) e) e) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (patch (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (patch (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) (patch (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) #<representation binary64>) () ()) |
#s(alt (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) (patch (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) #<representation binary64>) () ()) |
#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ()) |
#s(alt (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (cos.f64 v) (patch (cos.f64 v) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) (patch (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ()) |
#s(alt (/.f64 e (-.f64 #s(literal -1 binary64) e)) (patch (/.f64 e (-.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) (patch (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) (patch (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) (patch (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) (patch (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) #<representation binary64>) () ())) ()) |
#s(alt (/ v (+ 1 e)) (taylor 0 v) (#s(alt (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (patch (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* -1 (* (pow v 2) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (patch (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 e))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (patch (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* (pow v 2) (- (+ (* -1 (* (pow v 2) (+ (* -1/2 (/ (* e (- (* 1/120 (/ 1 (+ 1 e))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ 1 e))) (+ (* -1/24 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e))) (+ (* -1/720 (/ e (pow (+ 1 e) 2))) (* 1/5040 (/ 1 (+ 1 e)))))))) (* 1/120 (/ 1 (+ 1 e)))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) (taylor 0 v) (#s(alt (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) (patch (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt v (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* -1/6 (pow v 2)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 e) (taylor 0 v) (#s(alt (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (patch (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* -1/2 (* e (pow v 2))))) (taylor 0 v) (#s(alt (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (patch (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) (taylor 0 v) (#s(alt (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (patch (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) (taylor 0 v) (#s(alt (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (patch (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor 0 v) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) #<representation binary64>) () ())) ()) |
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#s(alt (* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) (taylor -inf e) (#s(alt (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) (patch (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 e) (taylor -inf e) (#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ())) ()) |
#s(alt (* -1 e) (taylor -inf e) (#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ())) ()) |
#s(alt (* -1 e) (taylor -inf e) (#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ())) ()) |
#s(alt (* -1 e) (taylor -inf e) (#s(alt (neg.f64 e) (patch (neg.f64 e) #<representation binary64>) () ())) ()) |
#s(alt (* e (* (cos v) (sin v))) (taylor -inf e) (#s(alt (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) (taylor -inf e) (#s(alt (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) (taylor -inf e) (#s(alt (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) (patch (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor -inf e) (#s(alt (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) (patch (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ())) ()) |
#s(alt (- 1 (* 2 (/ 1 e))) (taylor -inf e) (#s(alt (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) (patch (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ())) ()) |
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#s(alt -1 (taylor -inf e) (#s(alt (/.f64 e (-.f64 #s(literal -1 binary64) e)) (patch (/.f64 e (-.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
#s(alt (- (/ 1 e) 1) (taylor -inf e) (#s(alt (/.f64 e (-.f64 #s(literal -1 binary64) e)) (patch (/.f64 e (-.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
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#s(alt (- (* -1 (/ (- (* -1 (/ (- (/ 1 e) 1) e)) 1) e)) 1) (taylor -inf e) (#s(alt (/.f64 e (-.f64 #s(literal -1 binary64) e)) (patch (/.f64 e (-.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | e | @ | inf | ((* (/ (sin v) (+ (* (cos v) e) 1)) e) (/ (sin v) (+ (* (cos v) e) 1)) (sin v) (+ (* (cos v) e) 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* v e) (/ 1 (/ (+ 1 e) e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ 1 (/ (+ 1 e) e)) v) (/ (+ 1 e) e) (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (neg e) (* (sin v) (+ (* (cos v) e) -1))) (neg e) (* (sin v) (+ (* (cos v) e) -1)) (cos v) (* (/ e (- -1 e)) (/ e (- -1 e))) (/ e (- -1 e))) |
| 4.0ms | v | @ | -inf | ((* (/ (sin v) (+ (* (cos v) e) 1)) e) (/ (sin v) (+ (* (cos v) e) 1)) (sin v) (+ (* (cos v) e) 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* v e) (/ 1 (/ (+ 1 e) e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ 1 (/ (+ 1 e) e)) v) (/ (+ 1 e) e) (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (neg e) (* (sin v) (+ (* (cos v) e) -1))) (neg e) (* (sin v) (+ (* (cos v) e) -1)) (cos v) (* (/ e (- -1 e)) (/ e (- -1 e))) (/ e (- -1 e))) |
| 3.0ms | e | @ | -inf | ((* (/ (sin v) (+ (* (cos v) e) 1)) e) (/ (sin v) (+ (* (cos v) e) 1)) (sin v) (+ (* (cos v) e) 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* v e) (/ 1 (/ (+ 1 e) e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ 1 (/ (+ 1 e) e)) v) (/ (+ 1 e) e) (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (neg e) (* (sin v) (+ (* (cos v) e) -1))) (neg e) (* (sin v) (+ (* (cos v) e) -1)) (cos v) (* (/ e (- -1 e)) (/ e (- -1 e))) (/ e (- -1 e))) |
| 3.0ms | v | @ | 0 | ((* (/ (sin v) (+ (* (cos v) e) 1)) e) (/ (sin v) (+ (* (cos v) e) 1)) (sin v) (+ (* (cos v) e) 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* v e) (/ 1 (/ (+ 1 e) e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ 1 (/ (+ 1 e) e)) v) (/ (+ 1 e) e) (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (neg e) (* (sin v) (+ (* (cos v) e) -1))) (neg e) (* (sin v) (+ (* (cos v) e) -1)) (cos v) (* (/ e (- -1 e)) (/ e (- -1 e))) (/ e (- -1 e))) |
| 3.0ms | v | @ | inf | ((* (/ (sin v) (+ (* (cos v) e) 1)) e) (/ (sin v) (+ (* (cos v) e) 1)) (sin v) (+ (* (cos v) e) 1) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* v e) (/ 1 (/ (+ 1 e) e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ 1 (/ (+ 1 e) e)) v) (/ (+ 1 e) e) (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (neg e) (* (sin v) (+ (* (cos v) e) -1))) (neg e) (* (sin v) (+ (* (cos v) e) -1)) (cos v) (* (/ e (- -1 e)) (/ e (- -1 e))) (/ e (- -1 e))) |
| 1× | egg-herbie |
| 8 236× | lower-fma.f64 |
| 8 236× | lower-fma.f32 |
| 6 398× | lower-*.f64 |
| 6 398× | lower-*.f32 |
| 2 850× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 463 | 5965 |
| 1 | 1475 | 5741 |
| 2 | 4643 | 5653 |
| 0 | 8163 | 5331 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ v (+ 1 e)) |
(* v (+ (* -1 (* (pow v 2) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 e))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (* (pow v 2) (- (+ (* -1 (* (pow v 2) (+ (* -1/2 (/ (* e (- (* 1/120 (/ 1 (+ 1 e))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ 1 e))) (+ (* -1/24 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e))) (+ (* -1/720 (/ e (pow (+ 1 e) 2))) (* 1/5040 (/ 1 (+ 1 e)))))))) (* 1/120 (/ 1 (+ 1 e)))) (+ (* 1/24 (/ e (pow (+ 1 e) 2))) (* 1/2 (/ (* e (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e))))) (+ 1 e)))))) (+ (* -1/2 (/ e (pow (+ 1 e) 2))) (* 1/6 (/ 1 (+ 1 e)))))) (/ 1 (+ 1 e)))) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
(+ 1 e) |
(+ 1 (+ e (* -1/2 (* e (pow v 2))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* -1 (* e (* v (- e 1)))) |
(* v (+ (* -1 (* e (* (pow v 2) (+ (* -1/2 e) (* -1/6 (- e 1)))))) (* -1 (* e (- e 1))))) |
(* v (+ (* -1 (* e (- e 1))) (* (pow v 2) (+ (* -1 (* e (* (pow v 2) (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))))) (* -1 (* e (+ (* -1/2 e) (* -1/6 (- e 1))))))))) |
(* v (+ (* -1 (* e (- e 1))) (* (pow v 2) (+ (* -1 (* e (+ (* -1/2 e) (* -1/6 (- e 1))))) (* (pow v 2) (+ (* -1 (* e (* (pow v 2) (+ (* -1/144 e) (+ (* -1/240 e) (+ (* -1/720 e) (* -1/5040 (- e 1)))))))) (* -1 (* e (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e))))))))))) |
(* v (- e 1)) |
(* v (- (+ e (* (pow v 2) (+ (* -1/2 e) (* -1/6 (- e 1))))) 1)) |
(* v (- (+ e (* (pow v 2) (+ (* -1/2 e) (+ (* -1/6 (- e 1)) (* (pow v 2) (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (* 1/12 e)))))))) 1)) |
(* v (- (+ e (* (pow v 2) (+ (* -1/2 e) (+ (* -1/6 (- e 1)) (* (pow v 2) (+ (* 1/120 (- e 1)) (+ (* 1/24 e) (+ (* 1/12 e) (* (pow v 2) (+ (* -1/144 e) (+ (* -1/240 e) (+ (* -1/720 e) (* -1/5040 (- e 1)))))))))))))) 1)) |
1 |
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(+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/24 (* -1/720 (pow v 2)))) 1/2))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
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(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
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(* -1 (* e (* (sin v) (- (* e (cos v)) 1)))) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(cos v) |
(cos v) |
(cos v) |
(cos v) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(/ (sin v) (+ 1 (* e (cos v)))) |
(sin v) |
(sin v) |
(sin v) |
(sin v) |
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(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
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(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(/ (* e (sin v)) (+ 1 (* e (cos v)))) |
(* -1 (* e (* (sin v) (- (* e (cos v)) 1)))) |
(* -1 (* e (* (sin v) (- (* e (cos v)) 1)))) |
(* -1 (* e (* (sin v) (- (* e (cos v)) 1)))) |
(* -1 (* e (* (sin v) (- (* e (cos v)) 1)))) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(* (sin v) (- (* e (cos v)) 1)) |
(cos v) |
(cos v) |
(cos v) |
(cos v) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(sin v) |
(+ (sin v) (* -1 (* e (* (cos v) (sin v))))) |
(+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v))))) |
(+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v))))) |
1 |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(+ 1 (* e (cos v))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e v) |
(* e (+ v (* -1 (* e v)))) |
(* e (+ v (* e (- (* e v) v)))) |
(* e (+ v (* e (- (* e (- (* -1 (* e v)) (* -1 v))) v)))) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
e |
(* e (+ 1 (* -1 e))) |
(* e (+ 1 (* e (- e 1)))) |
(* e (+ 1 (* e (- (* e (+ 1 (* -1 e))) 1)))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e v) |
(* e (+ v (* -1 (* e v)))) |
(* e (+ v (* e (- (* e v) v)))) |
(* e (+ v (* e (- (* e (- (* -1 (* e v)) (* -1 v))) v)))) |
(/ 1 e) |
(/ (+ 1 e) e) |
(/ (+ 1 e) e) |
(/ (+ 1 e) e) |
e |
(* e (+ 1 (* -1 e))) |
(* e (+ 1 (* e (- e 1)))) |
(* e (+ 1 (* e (- (* e (+ 1 (* -1 e))) 1)))) |
(* -1 (pow e 2)) |
(* (pow e 2) (- (* 2 e) 1)) |
(* (pow e 2) (- (* e (+ 2 (* -3 e))) 1)) |
(* (pow e 2) (- (* e (+ 2 (* e (- (* 4 e) 3)))) 1)) |
(* -1 e) |
(* e (- e 1)) |
(* e (- (* e (+ 1 (* -1 e))) 1)) |
(* e (- (* e (+ 1 (* e (- e 1)))) 1)) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (* (pow (cos v) 2) (sin v))) (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* e (+ (sin v) (* -1 (* e (* (cos v) (sin v)))))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 (sin v)) |
(+ (* -1 (sin v)) (* e (* (cos v) (sin v)))) |
(+ (* -1 (sin v)) (* e (* (cos v) (sin v)))) |
(+ (* -1 (sin v)) (* e (* (cos v) (sin v)))) |
(pow e 2) |
(* (pow e 2) (+ 1 (* -2 e))) |
(* (pow e 2) (+ 1 (* e (- (* 3 e) 2)))) |
(* (pow e 2) (+ 1 (* e (- (* e (+ 3 (* -4 e))) 2)))) |
(* -1 e) |
(* e (- e 1)) |
(* e (- (* e (+ 1 (* -1 e))) 1)) |
(* e (- (* e (+ 1 (* e (- e 1)))) 1)) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ (sin v) (* e (cos v))) |
(/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) e) |
(/ (- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) e) |
(/ (- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) e) |
(* e (cos v)) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(* e (+ (cos v) (/ 1 e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
v |
(+ v (* -1 (/ v e))) |
(- (+ v (/ v (pow e 2))) (/ v e)) |
(- (+ v (* -1 (/ v (pow e 3)))) (+ (* -1 (/ v (pow e 2))) (/ v e))) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
1 |
(- 1 (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (+ (/ 1 e) (/ 1 (pow e 3)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
v |
(+ v (* -1 (/ v e))) |
(- (+ v (/ v (pow e 2))) (/ v e)) |
(- (+ v (* -1 (/ v (pow e 3)))) (+ (* -1 (/ v (pow e 2))) (/ v e))) |
1 |
(+ 1 (/ 1 e)) |
(+ 1 (/ 1 e)) |
(+ 1 (/ 1 e)) |
1 |
(- 1 (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (/ 1 e)) |
(- (+ 1 (/ 1 (pow e 2))) (+ (/ 1 e) (/ 1 (pow e 3)))) |
-1 |
(- (* 2 (/ 1 e)) 1) |
(- (* 2 (/ 1 e)) (+ 1 (/ 3 (pow e 2)))) |
(- (+ (* 2 (/ 1 e)) (* 4 (/ 1 (pow e 3)))) (+ 1 (/ 3 (pow e 2)))) |
-1 |
(- (/ 1 e) 1) |
(- (/ 1 e) (+ 1 (/ 1 (pow e 2)))) |
(- (+ (/ 1 e) (/ 1 (pow e 3))) (+ 1 (/ 1 (pow e 2)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(* -1 (* (pow e 2) (* (cos v) (sin v)))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* e (* (cos v) (sin v))) |
(* e (+ (* -1 (/ (sin v) e)) (* (cos v) (sin v)))) |
(* e (+ (* -1 (/ (sin v) e)) (* (cos v) (sin v)))) |
(* e (+ (* -1 (/ (sin v) e)) (* (cos v) (sin v)))) |
1 |
(- 1 (* 2 (/ 1 e))) |
(- (+ 1 (/ 3 (pow e 2))) (* 2 (/ 1 e))) |
(- (+ 1 (/ 3 (pow e 2))) (+ (* 2 (/ 1 e)) (* 4 (/ 1 (pow e 3))))) |
-1 |
(- (/ 1 e) 1) |
(- (/ 1 e) (+ 1 (/ 1 (pow e 2)))) |
(- (+ (/ 1 e) (/ 1 (pow e 3))) (+ 1 (/ 1 (pow e 2)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (* e (cos v))) |
(* -1 (/ (+ (* -1 (/ (sin v) (cos v))) (/ (sin v) (* e (pow (cos v) 2)))) e)) |
(* -1 (/ (+ (* -1 (/ (sin v) (cos v))) (* -1 (/ (- (/ (sin v) (* e (pow (cos v) 3))) (/ (sin v) (pow (cos v) 2))) e))) e)) |
(* -1 (/ (+ (* -1 (/ (sin v) (cos v))) (* -1 (/ (- (* -1 (/ (- (/ (sin v) (* e (pow (cos v) 4))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e))) e)) |
(* e (cos v)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
v |
(+ v (* -1 (/ v e))) |
(+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) |
(+ v (* -1 (/ (+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) e))) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
1 |
(- 1 (/ 1 e)) |
(+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) |
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
v |
(+ v (* -1 (/ v e))) |
(+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) |
(+ v (* -1 (/ (+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) e))) |
1 |
(+ 1 (/ 1 e)) |
(+ 1 (/ 1 e)) |
(+ 1 (/ 1 e)) |
1 |
(- 1 (/ 1 e)) |
(+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) |
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 e)) e))) e))) |
-1 |
(- (* 2 (/ 1 e)) 1) |
(- (* -1 (/ (- (* 3 (/ 1 e)) 2) e)) 1) |
(- (* -1 (/ (- (* -1 (/ (- (* 4 (/ 1 e)) 3) e)) 2) e)) 1) |
-1 |
(- (/ 1 e) 1) |
(- (* -1 (/ (- (/ 1 e) 1) e)) 1) |
(- (* -1 (/ (- (* -1 (/ (- (/ 1 e) 1) e)) 1) e)) 1) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(* -1 (* (pow e 2) (* (cos v) (sin v)))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* -1 e) |
(* e (* (cos v) (sin v))) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
1 |
(- 1 (* 2 (/ 1 e))) |
(+ 1 (* -1 (/ (- 2 (* 3 (/ 1 e))) e))) |
(+ 1 (* -1 (/ (+ 2 (* -1 (/ (- 3 (* 4 (/ 1 e))) e))) e))) |
-1 |
(- (/ 1 e) 1) |
(- (* -1 (/ (- (/ 1 e) 1) e)) 1) |
(- (* -1 (/ (- (* -1 (/ (- (/ 1 e) 1) e)) 1) e)) 1) |
| Outputs |
|---|
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 v (+.f64 #s(literal 1 binary64) e)) e) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 e (pow.f64 (+.f64 #s(literal 1 binary64) e) #s(literal 2 binary64)))) e (*.f64 (/.f64 e (+.f64 #s(literal 1 binary64) e)) #s(literal -1/6 binary64))) (*.f64 (/.f64 v (+.f64 #s(literal 1 binary64) e)) e)) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
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(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
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(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+.f64 (/.f64 (-.f64 (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) e) (/.f64 (sin.f64 v) (cos.f64 v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+.f64 (/.f64 (-.f64 (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) e) (/.f64 (sin.f64 v) (cos.f64 v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(* -1 (* (pow e 2) (* (cos v) (sin v)))) |
(*.f64 (*.f64 e (*.f64 (cos.f64 v) e)) (neg.f64 (sin.f64 v))) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)) |
(* (pow e 2) (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)) |
(* -1 e) |
(neg.f64 e) |
(* -1 e) |
(neg.f64 e) |
(* -1 e) |
(neg.f64 e) |
(* -1 e) |
(neg.f64 e) |
(* e (* (cos v) (sin v))) |
(*.f64 (*.f64 (cos.f64 v) e) (sin.f64 v)) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
(*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
(*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e) |
(* -1 (* e (+ (* -1 (* (cos v) (sin v))) (/ (sin v) e)))) |
(*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e) |
1 |
#s(literal 1 binary64) |
(- 1 (* 2 (/ 1 e))) |
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) e)) |
(+ 1 (* -1 (/ (- 2 (* 3 (/ 1 e))) e))) |
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 3 binary64) e)) e)) |
(+ 1 (* -1 (/ (+ 2 (* -1 (/ (- 3 (* 4 (/ 1 e))) e))) e))) |
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) e) #s(literal 3 binary64)) e) #s(literal 2 binary64)) e)) |
-1 |
#s(literal -1 binary64) |
(- (/ 1 e) 1) |
(-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) |
(- (* -1 (/ (- (/ 1 e) 1) e)) 1) |
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) |
(- (* -1 (/ (- (* -1 (/ (- (/ 1 e) 1) e)) 1) e)) 1) |
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)) |
| 4 664× | lower-/.f32 |
| 4 654× | lower-/.f64 |
| 3 726× | lower-fma.f32 |
| 3 722× | lower-fma.f64 |
| 3 284× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 242 |
| 0 | 62 | 189 |
| 1 | 260 | 189 |
| 2 | 1987 | 189 |
| 0 | 8376 | 189 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) |
(sin.f64 v) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 v e)) |
(*.f64 v e) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v) |
(/.f64 (+.f64 #s(literal 1 binary64) e) e) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
(-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) |
(+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
(*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64)))) |
(neg.f64 e) |
(*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(cos.f64 v) |
(*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e))) |
(/.f64 e (-.f64 #s(literal -1 binary64) e)) |
| Outputs |
|---|
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Compiled 58 484 to 8 243 computations (85.9% saved)
41 alts after pruning (35 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2 224 | 17 | 2 241 |
| Fresh | 7 | 18 | 25 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 2 233 | 41 | 2 274 |
| Status | Accuracy | Program |
|---|---|---|
| 72.0% | (pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| ▶ | 50.2% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
| 50.4% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 98.5% | (/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) | |
| 98.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) | |
| ✓ | 99.7% | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
| ▶ | 98.7% | (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
| 96.8% | (*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) | |
| 99.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (fma.f64 (pow.f64 e #s(literal -1/2 binary64)) (pow.f64 e #s(literal -1/2 binary64)) (cos.f64 v)))) | |
| ✓ | 99.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
| 96.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) | |
| 49.9% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) | |
| ▶ | 50.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
| ✓ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
| 37.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (pow.f64 (neg.f64 e) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 e e (*.f64 #s(literal 0 binary64) e)))) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) | |
| 27.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) | |
| 27.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) | |
| 27.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) | |
| 27.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) | |
| 63.8% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (sin.f64 v) (-.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) (pow.f64 e #s(literal -2 binary64)))) (-.f64 (cos.f64 v) (pow.f64 e #s(literal -1 binary64))))) | |
| 44.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| 43.4% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) | |
| ✓ | 50.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
| 48.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) | |
| 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 (neg.f64 e) (fma.f64 e (cos.f64 v) #s(literal -1 binary64))) (sin.f64 v))) | |
| ▶ | 99.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
| ✓ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
| 49.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) | |
| 49.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) | |
| 98.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e)))) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) | |
| 2.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) | |
| 50.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) | |
| 97.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) | |
| 2.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) | |
| ▶ | 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
| ✓ | 48.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
| 49.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
Compiled 1 115 to 851 computations (23.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) | |
| cost-diff | 0 | (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) | |
| cost-diff | 0 | #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) | |
| cost-diff | 0 | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| cost-diff | 320 | (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) | |
| cost-diff | 0 | (*.f64 e v) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) e) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) | |
| cost-diff | 1088 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) | |
| cost-diff | 0 | (-.f64 v (*.f64 v e)) | |
| cost-diff | 0 | (*.f64 (-.f64 v (*.f64 v e)) e) | |
| cost-diff | 0 | #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) | |
| cost-diff | 0 | (sin.f64 v) | |
| cost-diff | 0 | (neg.f64 (sin.f64 v)) | |
| cost-diff | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) | |
| cost-diff | 448 | (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
| 4 872× | lower-fma.f32 |
| 4 868× | lower-fma.f64 |
| 2 454× | lower-*.f32 |
| 2 436× | lower-*.f64 |
| 1 148× | unsub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 342 |
| 0 | 72 | 342 |
| 1 | 122 | 340 |
| 2 | 207 | 327 |
| 3 | 406 | 327 |
| 4 | 966 | 324 |
| 5 | 1636 | 324 |
| 6 | 2529 | 324 |
| 7 | 3414 | 324 |
| 8 | 6428 | 324 |
| 0 | 8234 | 308 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
(*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(neg.f64 (sin.f64 v)) |
(sin.f64 v) |
v |
(/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
#s(literal -1 binary64) |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(cos.f64 v) |
(/.f64 #s(literal -1 binary64) e) |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) |
(*.f64 (-.f64 v (*.f64 v e)) e) |
(-.f64 v (*.f64 v e)) |
v |
(*.f64 v e) |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) |
(+.f64 #s(literal 1 binary64) e) |
e |
(*.f64 e v) |
v |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v) |
(fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) |
(fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) |
(*.f64 (*.f64 v e) v) |
(*.f64 v e) |
v |
e |
#s(literal 1/120 binary64) |
(*.f64 #s(literal -1/6 binary64) e) |
#s(literal -1/6 binary64) |
(*.f64 v v) |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
(+.f64 e #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(sin.f64 v) |
v |
(/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) |
e |
#s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) |
(+.f64 #s(literal 1 binary64) e) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(neg.f64 (sin.f64 v)) |
(sin.f64 v) |
v |
(/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
#s(literal -1 binary64) |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(cos.f64 v) |
(/.f64 #s(literal -1 binary64) e) |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) |
(*.f64 (-.f64 v (*.f64 v e)) e) |
(-.f64 v (*.f64 v e)) |
v |
(*.f64 v e) |
e |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (-.f64 e #s(literal -1 binary64))) v)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) |
(*.f64 (/.f64 e (-.f64 e #s(literal -1 binary64))) v) |
#s(literal 1 binary64) |
(/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) |
(/.f64 (/.f64 (-.f64 e #s(literal -1 binary64)) v) e) |
(+.f64 #s(literal 1 binary64) e) |
(-.f64 e #s(literal -1 binary64)) |
e |
(*.f64 e v) |
(*.f64 v e) |
v |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/120 binary64) v) v #s(literal -1/6 binary64)) v) e)) #s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64)))) |
#s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) |
#s(approx (* e (sin v)) (*.f64 (fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/120 binary64) v) v #s(literal -1/6 binary64)) v) e)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v) |
(*.f64 (fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/120 binary64) v) v #s(literal -1/6 binary64)) v) e) |
(fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) |
(*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) v) v #s(literal -1/6 binary64)) v) v #s(literal 1 binary64)) e) |
(fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) v) v #s(literal -1/6 binary64)) e) |
(*.f64 (*.f64 v e) v) |
(*.f64 v e) |
v |
e |
#s(literal 1/120 binary64) |
(*.f64 #s(literal -1/6 binary64) e) |
#s(literal -1/6 binary64) |
(*.f64 v v) |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
#s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64))) |
(+.f64 e #s(literal 1 binary64)) |
(-.f64 e #s(literal -1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(*.f64 (/.f64 (sin.f64 v) #s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64)))) e) |
(sin.f64 v) |
v |
(/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) |
(/.f64 e #s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64)))) |
e |
#s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) |
#s(approx (+ 1 (* e (cos v))) (-.f64 e #s(literal -1 binary64))) |
(+.f64 #s(literal 1 binary64) e) |
(-.f64 e #s(literal -1 binary64)) |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (sin.f64 v) | |
| accuracy | 0.0234375 | (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) | |
| accuracy | 0.16796875 | (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) | |
| accuracy | 0.674999020658834 | #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) | |
| accuracy | 0.2803365266444272 | (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) | |
| accuracy | 0.34375 | (*.f64 #s(literal -1/6 binary64) e) | |
| accuracy | 0.674999020658834 | #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) | |
| accuracy | 31.868880484489488 | #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) | |
| accuracy | 0 | (*.f64 e v) | |
| accuracy | 0.25 | (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) | |
| accuracy | 0.6192311327198672 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) | |
| accuracy | 0 | (*.f64 v e) | |
| accuracy | 0.015625 | (*.f64 (-.f64 v (*.f64 v e)) e) | |
| accuracy | 0.9659718461219032 | #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) | |
| accuracy | 31.564734728088457 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) | |
| accuracy | 0 | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) | |
| accuracy | 0.0078125 | (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) | |
| accuracy | 0.16796875 | (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) | |
| accuracy | 0.18359375 | (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
| 89.0ms | 255× | 0 | valid |
| 0.0ms | 1× | 1 | valid |
Compiled 246 to 39 computations (84.1% saved)
ival-mult: 22.0ms (31.8% of total)const: 13.0ms (18.8% of total)ival-div: 11.0ms (15.9% of total)ival-add: 7.0ms (10.1% of total)ival-sin: 7.0ms (10.1% of total)ival-cos: 5.0ms (7.2% of total)ival-sub: 2.0ms (2.9% of total)ival-neg: 1.0ms (1.4% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) #<representation binary64>) () ()) |
#s(alt (neg.f64 (sin.f64 v)) (patch (neg.f64 (sin.f64 v)) #<representation binary64>) () ()) |
#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) #<representation binary64>) () ()) |
#s(alt (*.f64 (-.f64 v (*.f64 v e)) e) (patch (*.f64 (-.f64 v (*.f64 v e)) e) #<representation binary64>) () ()) |
#s(alt (-.f64 v (*.f64 v e)) (patch (-.f64 v (*.f64 v e)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) e) (patch (+.f64 #s(literal 1 binary64) e) #<representation binary64>) () ()) |
#s(alt (*.f64 e v) (patch (*.f64 e v) #<representation binary64>) () ()) |
#s(alt (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (patch (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) (patch (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) (patch #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #<representation binary64>) () ()) |
#s(alt (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) (patch (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) #<representation binary64>) () ()) |
#s(alt (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) (patch (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) #<representation binary64>) () ()) |
#s(alt (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) (patch (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) #<representation binary64>) () ()) |
#s(alt #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (patch #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) (patch (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) #<representation binary64>) () ()) |
#s(alt (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) (patch (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ()) |
#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ()) |
#s(alt (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) (patch (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) #<representation binary64>) () ()) |
#s(alt #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) (patch #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal -1/6 binary64) e) (patch (*.f64 #s(literal -1/6 binary64) e) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ v (+ 1 (/ 1 e))) (taylor 0 v) (#s(alt (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) (taylor 0 v) (#s(alt (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) (taylor 0 v) (#s(alt (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (+ (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (* (pow v 2) (- (* 1/720 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (+ (* -1/2 (/ (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))) (+ 1 (/ 1 e)))) (+ (* 1/5040 (/ 1 (+ 1 (/ 1 e)))) (* 1/24 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e))))))))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) (taylor 0 v) (#s(alt (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) (patch (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 v) (taylor 0 v) (#s(alt (neg.f64 (sin.f64 v)) (patch (neg.f64 (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- (* 1/6 (pow v 2)) 1)) (taylor 0 v) (#s(alt (neg.f64 (sin.f64 v)) (patch (neg.f64 (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1)) (taylor 0 v) (#s(alt (neg.f64 (sin.f64 v)) (patch (neg.f64 (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- (* (pow v 2) (+ 1/6 (* (pow v 2) (- (* 1/5040 (pow v 2)) 1/120)))) 1)) (taylor 0 v) (#s(alt (neg.f64 (sin.f64 v)) (patch (neg.f64 (sin.f64 v)) #<representation binary64>) () ())) ()) |
#s(alt v (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* -1/6 (pow v 2)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) (taylor 0 v) (#s(alt (sin.f64 v) (patch (sin.f64 v) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) #<representation binary64>) () ())) ()) |
#s(alt (* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) (taylor 0 v) (#s(alt #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) (patch #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) (patch #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) #<representation binary64>) () ())) ()) |
#s(alt (* e (* v (- 1 e))) (taylor 0 v) (#s(alt (*.f64 (-.f64 v (*.f64 v e)) e) (patch (*.f64 (-.f64 v (*.f64 v e)) e) #<representation binary64>) () ())) ()) |
#s(alt (* e (* v (- 1 e))) (taylor 0 v) (#s(alt (*.f64 (-.f64 v (*.f64 v e)) e) (patch (*.f64 (-.f64 v (*.f64 v e)) e) #<representation binary64>) () ())) ()) |
#s(alt (* e (* v (- 1 e))) (taylor 0 v) (#s(alt (*.f64 (-.f64 v (*.f64 v e)) e) (patch (*.f64 (-.f64 v (*.f64 v e)) e) #<representation binary64>) () ())) ()) |
#s(alt (* e (* v (- 1 e))) (taylor 0 v) (#s(alt (*.f64 (-.f64 v (*.f64 v e)) e) (patch (*.f64 (-.f64 v (*.f64 v e)) e) #<representation binary64>) () ())) ()) |
#s(alt (* v (- 1 e)) (taylor 0 v) (#s(alt (-.f64 v (*.f64 v e)) (patch (-.f64 v (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- 1 e)) (taylor 0 v) (#s(alt (-.f64 v (*.f64 v e)) (patch (-.f64 v (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- 1 e)) (taylor 0 v) (#s(alt (-.f64 v (*.f64 v e)) (patch (-.f64 v (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (* v (- 1 e)) (taylor 0 v) (#s(alt (-.f64 v (*.f64 v e)) (patch (-.f64 v (*.f64 v e)) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) #<representation binary64>) () ())) ()) |
#s(alt (/ (* e v) (+ 1 e)) (taylor 0 v) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) #<representation binary64>) () ())) ()) |
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#s(alt (+ (cos v) (/ 1 e)) (taylor -inf e) (#s(alt (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) (patch (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos v) (/ 1 e)) (taylor -inf e) (#s(alt (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) (patch (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
#s(alt (+ (cos v) (/ 1 e)) (taylor -inf e) (#s(alt (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) (patch (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor -inf e) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor -inf e) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor -inf e) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (* e v) (taylor -inf e) (#s(alt (*.f64 v e) (patch (*.f64 v e) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 v) (taylor -inf e) (#s(alt (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) (patch (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) #<representation binary64>) () ())) ()) |
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#s(alt (* e (cos v)) (taylor -inf e) (#s(alt #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) (patch #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1/6 e) (taylor -inf e) (#s(alt (*.f64 #s(literal -1/6 binary64) e) (patch (*.f64 #s(literal -1/6 binary64) e) #<representation binary64>) () ())) ()) |
#s(alt (* -1/6 e) (taylor -inf e) (#s(alt (*.f64 #s(literal -1/6 binary64) e) (patch (*.f64 #s(literal -1/6 binary64) e) #<representation binary64>) () ())) ()) |
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | v | @ | inf | ((* (neg (sin v)) (/ -1 (- (cos v) (/ -1 e)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (neg (sin v)) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* (- v (* v e)) e) (- v (* v e)) (/ 1 (/ (+ 1 e) (* e v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (+ 1 e) (* e v) (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ (* (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (* v v)) e) (* (sin v) (/ e (+ 1 (* e (cos v))))) (/ e (+ 1 (* e (cos v)))) (+ 1 (* e (cos v))) (/ -1 (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (* v e) (/ (+ 1 e) (* e v)) (+ 1 (* e (cos v))) (* -1/6 e)) |
| 5.0ms | e | @ | inf | ((* (neg (sin v)) (/ -1 (- (cos v) (/ -1 e)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (neg (sin v)) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* (- v (* v e)) e) (- v (* v e)) (/ 1 (/ (+ 1 e) (* e v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (+ 1 e) (* e v) (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ (* (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (* v v)) e) (* (sin v) (/ e (+ 1 (* e (cos v))))) (/ e (+ 1 (* e (cos v)))) (+ 1 (* e (cos v))) (/ -1 (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (* v e) (/ (+ 1 e) (* e v)) (+ 1 (* e (cos v))) (* -1/6 e)) |
| 5.0ms | v | @ | -inf | ((* (neg (sin v)) (/ -1 (- (cos v) (/ -1 e)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (neg (sin v)) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* (- v (* v e)) e) (- v (* v e)) (/ 1 (/ (+ 1 e) (* e v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (+ 1 e) (* e v) (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ (* (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (* v v)) e) (* (sin v) (/ e (+ 1 (* e (cos v))))) (/ e (+ 1 (* e (cos v)))) (+ 1 (* e (cos v))) (/ -1 (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (* v e) (/ (+ 1 e) (* e v)) (+ 1 (* e (cos v))) (* -1/6 e)) |
| 4.0ms | e | @ | -inf | ((* (neg (sin v)) (/ -1 (- (cos v) (/ -1 e)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (neg (sin v)) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* (- v (* v e)) e) (- v (* v e)) (/ 1 (/ (+ 1 e) (* e v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (+ 1 e) (* e v) (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ (* (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (* v v)) e) (* (sin v) (/ e (+ 1 (* e (cos v))))) (/ e (+ 1 (* e (cos v)))) (+ 1 (* e (cos v))) (/ -1 (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (* v e) (/ (+ 1 e) (* e v)) (+ 1 (* e (cos v))) (* -1/6 e)) |
| 4.0ms | v | @ | 0 | ((* (neg (sin v)) (/ -1 (- (cos v) (/ -1 e)))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (neg (sin v)) (sin v) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* (/ e (+ e 1)) v) (* (- v (* v e)) e) (- v (* v e)) (/ 1 (/ (+ 1 e) (* e v))) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (+ 1 e) (* e v) (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (/ (* e (sin v)) (+ 1 (* e (cos v)))) (* e (sin v)) (+ (* (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (* v v)) e) (* (sin v) (/ e (+ 1 (* e (cos v))))) (/ e (+ 1 (* e (cos v)))) (+ 1 (* e (cos v))) (/ -1 (- (cos v) (/ -1 e))) (- (cos v) (/ -1 e)) (* v e) (/ (+ 1 e) (* e v)) (+ 1 (* e (cos v))) (* -1/6 e)) |
| 1× | egg-herbie |
| 8 602× | lower-fma.f64 |
| 8 602× | lower-fma.f32 |
| 6 904× | lower-*.f64 |
| 6 904× | lower-*.f32 |
| 3 076× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 468 | 7253 |
| 1 | 1442 | 7047 |
| 2 | 4080 | 6965 |
| 0 | 8550 | 6629 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ v (+ 1 (/ 1 e))) |
(* v (+ (* (pow v 2) (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (+ (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (* (pow v 2) (- (* 1/720 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (+ (* -1/2 (/ (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))) (+ 1 (/ 1 e)))) (+ (* 1/5040 (/ 1 (+ 1 (/ 1 e)))) (* 1/24 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e))))))))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* -1 v) |
(* v (- (* 1/6 (pow v 2)) 1)) |
(* v (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1)) |
(* v (- (* (pow v 2) (+ 1/6 (* (pow v 2) (- (* 1/5040 (pow v 2)) 1/120)))) 1)) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* e (* v (- 1 e))) |
(* e (* v (- 1 e))) |
(* e (* v (- 1 e))) |
(* e (* v (- 1 e))) |
(* v (- 1 e)) |
(* v (- 1 e)) |
(* v (- 1 e)) |
(* v (- 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(* -1/6 e) |
(+ (* -1/6 e) (* 1/120 (* e (pow v 2)))) |
(+ (* -1/6 e) (* 1/120 (* e (pow v 2)))) |
(+ (* -1/6 e) (* 1/120 (* e (pow v 2)))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* e v) |
(* v (+ e (* -1/6 (* e (pow v 2))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2))))))) |
(* v (+ e (* (pow v 2) (+ (* -1/6 e) (* (pow v 2) (+ (* -1/5040 (* e (pow v 2))) (* 1/120 e))))))) |
e |
(+ e (* -1/6 (* e (pow v 2)))) |
(+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2)))))) |
(+ e (* (pow v 2) (+ (* -1/6 e) (* 1/120 (* e (pow v 2)))))) |
(/ (* e v) (+ 1 e)) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(/ e (+ 1 e)) |
(+ (* 1/2 (/ (* (pow e 2) (pow v 2)) (pow (+ 1 e) 2))) (/ e (+ 1 e))) |
(+ (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -1/4 (/ (pow e 3) (pow (+ 1 e) 3))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e))) |
(+ (* (pow v 2) (- (* (pow v 2) (- (* -1 (* (pow v 2) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (+ (* 1/48 (/ (pow e 3) (pow (+ 1 e) 3))) (* 1/2 (/ (* e (+ (* -1/4 (/ (pow e 3) (pow (+ 1 e) 3))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))))))) (+ (* -1/4 (/ (pow e 3) (pow (+ 1 e) 3))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e))) |
(+ 1 e) |
(+ 1 (+ e (* -1/2 (* e (pow v 2))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* 1/24 (* e (pow v 2))))))) |
(+ 1 (+ e (* (pow v 2) (+ (* -1/2 e) (* (pow v 2) (+ (* -1/720 (* e (pow v 2))) (* 1/24 e))))))) |
(/ -1 (+ 1 (/ 1 e))) |
(- (* -1/2 (/ (pow v 2) (pow (+ 1 (/ 1 e)) 2))) (/ 1 (+ 1 (/ 1 e)))) |
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(* e v) |
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v |
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(* e v) |
(* e (+ v (* -1 (* e v)))) |
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(* e (sin v)) |
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1 |
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(+ 1 e) |
(+ 1 e) |
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(* e v) |
(* e v) |
(* e v) |
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(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
(* e (sin v)) |
(* e (sin v)) |
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(* e (sin v)) |
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(* e (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* e (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* e (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(* e (sin v)) |
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(* e (+ (sin v) (* e (- (* e (- (* -1 (* e (* (pow (cos v) 3) (sin v)))) (* -1 (* (pow (cos v) 2) (sin v))))) (* (cos v) (sin v)))))) |
e |
(* e (+ 1 (* -1 (* e (cos v))))) |
(* e (+ 1 (* e (- (* e (pow (cos v) 2)) (cos v))))) |
(* e (+ 1 (* e (- (* e (- (* -1 (* e (pow (cos v) 3))) (* -1 (pow (cos v) 2)))) (cos v))))) |
1 |
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(+ 1 (* e (cos v))) |
(* -1 e) |
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(* e (- (* e (- (* -1 (* e (pow (cos v) 2))) (* -1 (cos v)))) 1)) |
(* e (- (* e (- (* e (- (* e (pow (cos v) 3)) (pow (cos v) 2))) (* -1 (cos v)))) 1)) |
(/ 1 e) |
(/ (+ 1 (* e (cos v))) e) |
(/ (+ 1 (* e (cos v))) e) |
(/ (+ 1 (* e (cos v))) e) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ 1 (* e v)) |
(/ (+ (/ 1 v) (/ e v)) e) |
(/ (+ (/ 1 v) (/ e v)) e) |
(/ (+ (/ 1 v) (/ e v)) e) |
1 |
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(+ 1 (* e (cos v))) |
(* -1/6 e) |
(* -1/6 e) |
(* -1/6 e) |
(* -1/6 e) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
v |
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(- (+ v (/ v (pow e 2))) (/ v e)) |
(- (+ v (* -1 (/ v (pow e 3)))) (+ (* -1 (/ v (pow e 2))) (/ v e))) |
(* -1 (* (pow e 2) v)) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* -1 (* e v)) |
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(* e (- (/ v e) v)) |
v |
(+ v (* -1 (/ v e))) |
(- (+ v (/ v (pow e 2))) (/ v e)) |
(- (+ v (* -1 (/ v (pow e 3)))) (+ (* -1 (/ v (pow e 2))) (/ v e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
e |
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(* e v) |
(* e v) |
(* e v) |
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(/ (sin v) (cos v)) |
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(- (+ (/ (sin v) (cos v)) (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2)))) |
(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
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(/ (sin v) (cos v)) |
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(- (+ (* -1 (/ (sin v) (* (pow e 3) (pow (cos v) 4)))) (/ (sin v) (cos v))) (+ (* -1 (/ (sin v) (* (pow e 2) (pow (cos v) 3)))) (/ (sin v) (* e (pow (cos v) 2))))) |
(/ 1 (cos v)) |
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(- (+ (/ 1 (cos v)) (/ 1 (* (pow e 2) (pow (cos v) 3)))) (+ (/ 1 (* e (pow (cos v) 2))) (/ 1 (* (pow e 3) (pow (cos v) 4))))) |
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(/ -1 (cos v)) |
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(- (+ (/ 1 (* e (pow (cos v) 2))) (/ 1 (* (pow e 3) (pow (cos v) 4)))) (+ (/ 1 (cos v)) (/ 1 (* (pow e 2) (pow (cos v) 3))))) |
(cos v) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ 1 v) |
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(* -1/6 e) |
(* -1/6 e) |
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(* -1/6 e) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (* -1 (/ (sin v) (pow (cos v) 3)))) e)) (* -1 (/ (sin v) (pow (cos v) 2)))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (cos v)) |
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(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
v |
(+ v (* -1 (/ v e))) |
(+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) |
(+ v (* -1 (/ (+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) e))) |
(* -1 (* (pow e 2) v)) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* (pow e 2) (+ (* -1 v) (/ v e))) |
(* -1 (* e v)) |
(* -1 (* e (- (* -1 (/ v e)) (* -1 v)))) |
(* -1 (* e (- (* -1 (/ v e)) (* -1 v)))) |
(* -1 (* e (- (* -1 (/ v e)) (* -1 v)))) |
v |
(+ v (* -1 (/ v e))) |
(+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) |
(+ v (* -1 (/ (+ v (* -1 (/ (+ v (* -1 (/ v e))) e))) e))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
e |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(* e (+ 1 (/ 1 e))) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* e (sin v)) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(/ (sin v) (cos v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(/ 1 (cos v)) |
(- (/ 1 (cos v)) (/ 1 (* e (pow (cos v) 2)))) |
(+ (* -1 (/ (- (/ 1 (pow (cos v) 2)) (/ 1 (* e (pow (cos v) 3)))) e)) (/ 1 (cos v))) |
(+ (* -1 (/ (+ (* -1 (/ (- (/ 1 (pow (cos v) 3)) (/ 1 (* e (pow (cos v) 4)))) e)) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(* e (cos v)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(/ -1 (cos v)) |
(- (/ 1 (* e (pow (cos v) 2))) (/ 1 (cos v))) |
(- (* -1 (/ (- (/ 1 (* e (pow (cos v) 3))) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(- (* -1 (/ (- (* -1 (/ (- (/ 1 (* e (pow (cos v) 4))) (/ 1 (pow (cos v) 3))) e)) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(cos v) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(+ (cos v) (/ 1 e)) |
(* e v) |
(* e v) |
(* e v) |
(* e v) |
(/ 1 v) |
(+ (/ 1 v) (/ 1 (* e v))) |
(+ (/ 1 v) (/ 1 (* e v))) |
(+ (/ 1 v) (/ 1 (* e v))) |
(* e (cos v)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(* -1/6 e) |
(* -1/6 e) |
(* -1/6 e) |
(* -1/6 e) |
| Outputs |
|---|
(/ v (+ 1 (/ 1 e))) |
(/.f64 v (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))) |
(* v (+ (* (pow v 2) (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) (/.f64 v (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/24 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))))) (*.f64 v v) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))))) (/.f64 v (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) |
(* v (+ (* (pow v 2) (- (+ (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* (pow v 2) (- (+ (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (* (pow v 2) (- (* 1/720 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (+ (* -1/2 (/ (- (* 1/120 (/ 1 (+ 1 (/ 1 e)))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))) (+ 1 (/ 1 e)))) (+ (* 1/5040 (/ 1 (+ 1 (/ 1 e)))) (* 1/24 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e))))))))) (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow (+ 1 (/ 1 e)) 2))) (* 1/6 (/ 1 (+ 1 (/ 1 e))))) (+ 1 (/ 1 e)))) (* 1/24 (/ 1 (pow (+ 1 (/ 1 e)) 2))))))) (* 1/6 (/ 1 (+ 1 (/ 1 e)))))) (/ 1 (+ 1 (/ 1 e))))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/720 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/24 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))))) (*.f64 v v) (-.f64 (/.f64 #s(literal 1/120 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))) (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/24 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64)))))) (*.f64 v v) (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64))))) (/.f64 v (+.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64)))) (*.f64 v v) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 v v) (/.f64 e (+.f64 e #s(literal 1 binary64)))) v) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal -1/5040 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64)))) (fma.f64 (*.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64)))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) e) (/.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (+.f64 e #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 #s(literal -1/720 binary64) e) e) (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))))) (*.f64 v v) (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64))))) (*.f64 v v) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(* -1 v) |
(neg.f64 v) |
(* v (- (* 1/6 (pow v 2)) 1)) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 v v) #s(literal -1 binary64)) v) |
(* v (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1)) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64)) v) |
(* v (- (* (pow v 2) (+ 1/6 (* (pow v 2) (- (* 1/5040 (pow v 2)) 1/120)))) 1)) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 v v) #s(literal -1/120 binary64)) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64)) v) |
v |
(* v (+ 1 (* -1/6 (pow v 2)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) #s(literal -1/6 binary64) v) |
(* v (+ 1 (* (pow v 2) (- (* 1/120 (pow v 2)) 1/6)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) v) |
(* v (+ 1 (* (pow v 2) (- (* (pow v 2) (+ 1/120 (* -1/5040 (pow v 2)))) 1/6)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 v v) #s(literal 1/120 binary64)) (*.f64 v v) #s(literal -1/6 binary64)) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64)))) (*.f64 v v) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 v v) (/.f64 e (+.f64 e #s(literal 1 binary64)))) v) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (+ (* 1/120 (/ e (+ 1 e))) (* (pow v 2) (- (* -1/5040 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2)))))) (+ 1 e))) (+ (* -1/720 (/ (pow e 2) (pow (+ 1 e) 2))) (* 1/24 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e)))))))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal -1/5040 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64)))) (fma.f64 (*.f64 (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64)))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/24 binary64) e) (/.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (+.f64 e #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 #s(literal -1/720 binary64) e) e) (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))))) (*.f64 v v) (fma.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal 1/120 binary64) (fma.f64 #s(literal -1/24 binary64) (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (/.f64 e (+.f64 e #s(literal 1 binary64)))) #s(literal 1/2 binary64))))) (*.f64 v v) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(* e (* v (- 1 e))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e) |
(* e (* v (- 1 e))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e) |
(* e (* v (- 1 e))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e) |
(* e (* v (- 1 e))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e) |
(* v (- 1 e)) |
(*.f64 (-.f64 #s(literal 1 binary64) e) v) |
(* v (- 1 e)) |
(*.f64 (-.f64 #s(literal 1 binary64) e) v) |
(* v (- 1 e)) |
(*.f64 (-.f64 #s(literal 1 binary64) e) v) |
(* v (- 1 e)) |
(*.f64 (-.f64 #s(literal 1 binary64) e) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(/ (* e v) (+ 1 e)) |
(*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v) |
(* v (+ (* (pow v 2) (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
(fma.f64 (pow.f64 v #s(literal 3 binary64)) (fma.f64 (*.f64 e (/.f64 e (pow.f64 (+.f64 e #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
(* v (+ (* (pow v 2) (- (+ (* -1/6 (/ e (+ 1 e))) (* (pow v 2) (- (* 1/120 (/ e (+ 1 e))) (+ (* -1/2 (/ (* e (- (* -1/6 (/ e (+ 1 e))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (+ 1 e))) (* 1/24 (/ (pow e 2) (pow (+ 1 e) 2))))))) (* -1/2 (/ (pow e 2) (pow (+ 1 e) 2))))) (/ e (+ 1 e)))) |
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(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
e |
(* e (+ 1 (/ 1 e))) |
(+.f64 e #s(literal 1 binary64)) |
(* e (+ 1 (/ 1 e))) |
(+.f64 e #s(literal 1 binary64)) |
(* e (+ 1 (/ 1 e))) |
(+.f64 e #s(literal 1 binary64)) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e) |
(* -1 (* e (+ 1/6 (* -1/120 (pow v 2))))) |
(*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* e (sin v)) |
(*.f64 (sin.f64 v) e) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(*.f64 (neg.f64 e) (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(*.f64 (neg.f64 e) (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(*.f64 (neg.f64 e) (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64))) |
(* -1 (* e (- (* (pow v 2) (+ 1/6 (* -1/120 (pow v 2)))) 1))) |
(*.f64 (neg.f64 e) (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 v v) #s(literal 1/6 binary64)) (*.f64 v v) #s(literal -1 binary64))) |
(/ (sin v) (cos v)) |
(/.f64 (sin.f64 v) (cos.f64 v)) |
(+ (* -1 (/ (sin v) (* e (pow (cos v) 2)))) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) |
(+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 3)))) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin v) (* e (pow (cos v) 4)))) (/ (sin v) (pow (cos v) 3))) e)) (/ (sin v) (pow (cos v) 2))) e)) (/ (sin v) (cos v))) |
(-.f64 (/.f64 (sin.f64 v) (cos.f64 v)) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (sin.f64 v) (pow.f64 (cos.f64 v) #s(literal 3 binary64))) (/.f64 (/.f64 (sin.f64 v) e) (pow.f64 (cos.f64 v) #s(literal 4 binary64)))) e)) e)) |
(/ 1 (cos v)) |
(/.f64 #s(literal 1 binary64) (cos.f64 v)) |
(- (/ 1 (cos v)) (/ 1 (* e (pow (cos v) 2)))) |
(-.f64 (/.f64 #s(literal 1 binary64) (cos.f64 v)) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e))) |
(+ (* -1 (/ (- (/ 1 (pow (cos v) 2)) (/ 1 (* e (pow (cos v) 3)))) e)) (/ 1 (cos v))) |
(-.f64 (/.f64 #s(literal 1 binary64) (cos.f64 v)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 3 binary64)) e))) e)) |
(+ (* -1 (/ (+ (* -1 (/ (- (/ 1 (pow (cos v) 3)) (/ 1 (* e (pow (cos v) 4)))) e)) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 4 binary64)) e)) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) e) (/.f64 #s(literal 1 binary64) (cos.f64 v))) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(/ -1 (cos v)) |
(/.f64 #s(literal -1 binary64) (cos.f64 v)) |
(- (/ 1 (* e (pow (cos v) 2))) (/ 1 (cos v))) |
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) e)) (/.f64 #s(literal 1 binary64) (cos.f64 v))) |
(- (* -1 (/ (- (/ 1 (* e (pow (cos v) 3))) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(-.f64 (/.f64 #s(literal -1 binary64) (cos.f64 v)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 3 binary64)) e)) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 v) #s(literal 2 binary64)))) e)) |
(- (* -1 (/ (- (* -1 (/ (- (/ 1 (* e (pow (cos v) 4))) (/ 1 (pow (cos v) 3))) e)) (/ 1 (pow (cos v) 2))) e)) (/ 1 (cos v))) |
(-.f64 (/.f64 #s(literal -1 binary64) (cos.f64 v)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 v) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 v) #s(literal 4 binary64)) e)) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 v) #s(literal 3 binary64)))) e)) e)) |
(cos v) |
(cos.f64 v) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(+ (cos v) (/ 1 e)) |
(+.f64 (cos.f64 v) (/.f64 #s(literal 1 binary64) e)) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(* e v) |
(*.f64 e v) |
(/ 1 v) |
(/.f64 #s(literal 1 binary64) v) |
(+ (/ 1 v) (/ 1 (* e v))) |
(+.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 (/.f64 #s(literal 1 binary64) e) v)) |
(+ (/ 1 v) (/ 1 (* e v))) |
(+.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 (/.f64 #s(literal 1 binary64) e) v)) |
(+ (/ 1 v) (/ 1 (* e v))) |
(+.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 (/.f64 #s(literal 1 binary64) e) v)) |
(* e (cos v)) |
(*.f64 (cos.f64 v) e) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1 (* e (- (* -1 (cos v)) (/ 1 e)))) |
(fma.f64 (cos.f64 v) e #s(literal 1 binary64)) |
(* -1/6 e) |
(*.f64 #s(literal -1/6 binary64) e) |
(* -1/6 e) |
(*.f64 #s(literal -1/6 binary64) e) |
(* -1/6 e) |
(*.f64 #s(literal -1/6 binary64) e) |
(* -1/6 e) |
(*.f64 #s(literal -1/6 binary64) e) |
| 4 190× | lower-/.f32 |
| 4 178× | lower-/.f64 |
| 3 760× | lower-fma.f32 |
| 3 756× | lower-fma.f64 |
| 3 592× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 285 |
| 0 | 72 | 285 |
| 1 | 262 | 279 |
| 2 | 1645 | 275 |
| 0 | 8579 | 267 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
(neg.f64 (sin.f64 v)) |
(sin.f64 v) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e)) |
(*.f64 (-.f64 v (*.f64 v e)) e) |
(-.f64 v (*.f64 v e)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
(+.f64 #s(literal 1 binary64) e) |
(*.f64 e v) |
(fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) |
(fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) |
#s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) |
(/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))) |
(-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)) |
(*.f64 v e) |
(/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)) |
#s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64))) |
(*.f64 #s(literal -1/6 binary64) e) |
| Outputs |
|---|
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Compiled 25 821 to 3 371 computations (86.9% saved)
47 alts after pruning (38 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 257 | 13 | 1 270 |
| Fresh | 5 | 25 | 30 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 6 | 6 |
| Total | 1 264 | 47 | 1 311 |
| Status | Accuracy | Program |
|---|---|---|
| 72.0% | (pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) | |
| 50.4% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 50.2% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 50.4% | (/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) | |
| 98.5% | (/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) | |
| 98.0% | (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) | |
| 73.2% | (*.f64 (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 v) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (sin.f64 v) #s(literal 2 binary64)) #s(literal 0 binary64)))) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) | |
| ✓ | 99.7% | (*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
| ✓ | 98.7% | (*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
| 98.3% | (*.f64 (sin.f64 v) #s(approx (/ e (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e))) | |
| 96.8% | (*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) | |
| 99.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (fma.f64 (pow.f64 e #s(literal -1/2 binary64)) (pow.f64 e #s(literal -1/2 binary64)) (cos.f64 v)))) | |
| ✓ | 99.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
| 96.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) | |
| 50.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) | |
| 48.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) | |
| 49.9% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) | |
| 48.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) | |
| ✓ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
| 37.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (pow.f64 (neg.f64 e) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 e e (*.f64 #s(literal 0 binary64) e)))) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) | |
| 27.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) | |
| 27.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) | |
| 27.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) | |
| 27.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) | |
| 63.8% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (sin.f64 v) (-.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) (pow.f64 e #s(literal -2 binary64)))) (-.f64 (cos.f64 v) (pow.f64 e #s(literal -1 binary64))))) | |
| 44.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| 43.4% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) | |
| 50.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) | |
| ✓ | 50.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
| ✓ | 99.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
| 96.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e))))) | |
| ✓ | 98.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
| 49.2% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) | |
| 49.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) | |
| 98.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e)))) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) | |
| 50.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) | |
| 97.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) | |
| 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) | |
| 49.5% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) | |
| ✓ | 49.6% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
| 49.1% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) | |
| 27.0% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) | |
| ✓ | 48.7% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
| 49.3% | #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
Compiled 1 649 to 861 computations (47.8% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
(*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) |
(/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 e (fma.f64 (cos.f64 v) (neg.f64 e) #s(literal 1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 (neg.f64 e) (fma.f64 e (cos.f64 v) #s(literal -1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) #s(approx (/ e (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e))) |
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 e (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) (*.f64 (sin.f64 v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (pow.f64 (neg.f64 e) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 e e (*.f64 #s(literal 0 binary64) e)))) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (fma.f64 (pow.f64 e #s(literal -1/2 binary64)) (pow.f64 e #s(literal -1/2 binary64)) (cos.f64 v)))) |
(pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(*.f64 (/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 v) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (sin.f64 v) #s(literal 2 binary64)) #s(literal 0 binary64)))) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (sin.f64 v) (-.f64 (pow.f64 (cos.f64 v) #s(literal 2 binary64)) (pow.f64 e #s(literal -2 binary64)))) (-.f64 (cos.f64 v) (pow.f64 e #s(literal -1 binary64))))) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (neg.f64 e) (sin.f64 v)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 v) e) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 (neg.f64 e) (sin.f64 v)))))) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
3 calls:
| 23.0ms | v |
| 21.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 20.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | e |
| 99.7% | 1 | v |
| 99.7% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
(*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) |
(/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 e (fma.f64 (cos.f64 v) (neg.f64 e) #s(literal 1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 (neg.f64 e) (fma.f64 e (cos.f64 v) #s(literal -1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) #s(approx (/ e (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e))) |
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e)))) |
(/.f64 e (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (*.f64 (sin.f64 v) (+.f64 (/.f64 #s(literal -1 binary64) e) (cos.f64 v))) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 v) (/.f64 #s(literal -1 binary64) e))))) |
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 (cos.f64 v) e)) (*.f64 (sin.f64 v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (fma.f64 (neg.f64 (sin.f64 v)) (cos.f64 v) (/.f64 (sin.f64 v) e)) (*.f64 e e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (pow.f64 (neg.f64 e) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 e e (*.f64 #s(literal 0 binary64) e)))) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) (fma.f64 (pow.f64 e #s(literal -1/2 binary64)) (pow.f64 e #s(literal -1/2 binary64)) (cos.f64 v)))) |
(pow.f64 (pow.f64 (/.f64 (/.f64 (fma.f64 (cos.f64 v) e #s(literal 1 binary64)) e) (sin.f64 v)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
3 calls:
| 23.0ms | v |
| 20.0ms | e |
| 18.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | e |
| 99.7% | 1 | v |
| 99.7% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
(*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(/.f64 (*.f64 e (sin.f64 v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 (sin.f64 v) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e)))) |
(/.f64 e (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 (sin.f64 v)) (/.f64 #s(literal -1 binary64) #s(approx (- (cos v) (/ -1 e)) (/.f64 #s(literal 1 binary64) e))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (fma.f64 (pow.f64 v #s(literal 3 binary64)) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 e (+.f64 e #s(literal 1 binary64))) #s(literal -1/6 binary64))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) (*.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 e (fma.f64 (cos.f64 v) (neg.f64 e) #s(literal 1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (*.f64 (neg.f64 e) (fma.f64 e (cos.f64 v) #s(literal -1 binary64))) (sin.f64 v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) (*.f64 (sin.f64 v) e))) |
(*.f64 (sin.f64 v) #s(approx (/ e (+ 1 (* e (cos v)))) (*.f64 (fma.f64 (neg.f64 e) (cos.f64 v) #s(literal 1 binary64)) e))) |
| Outputs |
|---|
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
3 calls:
| 497.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 19.0ms | v |
| 16.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | e |
| 98.7% | 1 | v |
| 98.7% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
(*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
3 calls:
| 19.0ms | e |
| 13.0ms | v |
| 13.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | e |
| 97.6% | 1 | v |
| 97.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
(*.f64 #s(approx (/ (sin v) (+ (* (cos v) e) 1)) (sin.f64 v)) e) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e)) |
3 calls:
| 12.0ms | v |
| 12.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 11.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.8% | 1 | e |
| 98.7% | 2 | v |
| 96.8% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (-.f64 (/.f64 v e) v) e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) e) e #s(literal -1 binary64)) e #s(literal 1 binary64)) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 v (/.f64 (+.f64 #s(literal 1 binary64) e) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) e) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 e) #s(literal 1 binary64)) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (/.f64 e (/.f64 #s(literal 1 binary64) (-.f64 v (*.f64 e v)))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) e) (*.f64 e v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1 e) (* e v)) (/.f64 (/.f64 #s(literal 1 binary64) e) v)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal -1/6 binary64) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (+ (* (neg e) (cos v)) 1) (* (sin v) e)) (*.f64 (*.f64 v e) (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) e (fma.f64 #s(literal 1/6 binary64) e #s(literal -1/6 binary64))) v) v (-.f64 #s(literal 1 binary64) e))))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (/.f64 (fma.f64 e e #s(literal -1 binary64)) (-.f64 e #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) e) v))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64))) (*.f64 v v) e) #s(literal 1 binary64)) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (neg.f64 e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) v) (/.f64 (+.f64 #s(literal 1 binary64) e) (neg.f64 e))))) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 #s(approx (+ (* (* (* v e) v) 1/120) (* -1/6 e)) (*.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 v v) #s(literal -1/6 binary64)) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 #s(approx (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (*.f64 (*.f64 (fma.f64 #s(literal 2 binary64) e #s(literal -1 binary64)) e) e)) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
(/.f64 #s(approx (* e (sin v)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 v e) v) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) e)) (*.f64 v v) e) v)) #s(approx (+ 1 (* e (cos v))) (+.f64 e #s(literal 1 binary64)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) #s(literal -1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 #s(literal 1 binary64) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) (+.f64 #s(literal 0 binary64) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (neg.f64 e) #s(approx (* (sin v) (+ (* (cos v) e) -1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/8 binary64) e (fma.f64 (*.f64 (fma.f64 e #s(literal -1/80 binary64) (fma.f64 #s(literal -1/5040 binary64) e #s(literal 1/5040 binary64))) v) v (fma.f64 #s(literal 1/120 binary64) e #s(literal -1/120 binary64)))) (*.f64 v v) (fma.f64 #s(literal -1/2 binary64) e (fma.f64 #s(literal -1/6 binary64) e #s(literal 1/6 binary64)))) (*.f64 v v) (-.f64 e #s(literal 1 binary64))) v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 e (-.f64 #s(literal -1 binary64) e)) (/.f64 e (-.f64 #s(literal -1 binary64) e)))) #s(approx (+ 0 (/ e (- -1 e))) (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e)) e) #s(literal 1 binary64)) e)))) v)) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
3 calls:
| 13.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 12.0ms | v |
| 11.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 50.7% | 1 | e |
| 50.7% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 50.7% | 1 | v |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) e))) v)) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
3 calls:
| 4.0ms | e |
| 4.0ms | v |
| 4.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.6% | 1 | e |
| 49.6% | 1 | v |
| 49.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (-.f64 v (/.f64 v e)))) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
3 calls:
| 3.0ms | v |
| 3.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 3.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.6% | 1 | e |
| 49.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 49.6% | 1 | v |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
3 calls:
| 3.0ms | v |
| 2.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 2.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.6% | 1 | e |
| 49.6% | 1 | v |
| 49.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
3 calls:
| 2.0ms | v |
| 2.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 2.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.6% | 1 | e |
| 49.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 49.6% | 1 | v |
Compiled 13 to 13 computations (0% saved)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
3 calls:
| 3.0ms | v |
| 2.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 2.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 49.6% | 1 | e |
| 49.6% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 49.6% | 1 | v |
Compiled 13 to 13 computations (0% saved)
Total -14.7b remaining (-44.8%)
Threshold costs -14.7b (-44.8%)
| Inputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 #s(approx (- v (* v e)) (*.f64 (neg.f64 e) v)) e))) |
| Outputs |
|---|
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
3 calls:
| 2.0ms | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 2.0ms | v |
| 2.0ms | e |
| Accuracy | Segments | Branch |
|---|---|---|
| 48.7% | 1 | e |
| 48.7% | 1 | (/.f64 (*.f64 e (sin.f64 v)) (+.f64 #s(literal 1 binary64) (*.f64 e (cos.f64 v)))) |
| 48.7% | 1 | v |
Compiled 13 to 13 computations (0% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 17.0ms | 2.2351047231365252e-13 | 3.667532426534133e-6 |
| 11.0ms | 144× | 0 | valid |
Compiled 131 to 140 computations (-6.9% saved)
ival-mult: 2.0ms (28.7% of total)ival-sin: 2.0ms (28.7% of total)ival-div: 1.0ms (14.4% of total)ival-add: 1.0ms (14.4% of total)ival-cos: 1.0ms (14.4% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 46× | *-commutative-binary64-*.f64 |
| 22× | +-commutative-binary64-+.f64 |
| 20× | sub-neg-binary64-neg.f64-+.f64--.f64 |
| 14× | neg-sub0-binary64--.f64-neg.f64 |
| 14× | neg-mul-1-binary64-*.f64-neg.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 78 | 302 |
| 1 | 113 | 302 |
| 2 | 133 | 302 |
| 3 | 151 | 302 |
| 4 | 156 | 302 |
| 5 | 157 | 302 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
(if (<=.f64 v #s(literal 4457913959828945/151115727451828646838272 binary64)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
| Outputs |
|---|
(*.f64 (/.f64 (*.f64 (sin.f64 v) e) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (cos.f64 v) e #s(literal -1 binary64))) |
(*.f64 (fma.f64 (cos.f64 v) e #s(literal -1 binary64)) (/.f64 (*.f64 e (sin.f64 v)) (-.f64 (pow.f64 (*.f64 (cos.f64 v) e) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (sin.f64 v) (fma.f64 (cos.f64 v) e #s(literal 1 binary64))) e) |
(*.f64 (sin.f64 v) (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e)))) |
(*.f64 (/.f64 e #s(approx (+ 1 (* e (cos v))) (+.f64 #s(literal 1 binary64) e))) (sin.f64 v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 (sin.f64 v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (+ (* (neg e) (cos v)) 1) (-.f64 #s(literal 1 binary64) e)) (*.f64 e (sin.f64 v)))) |
(if (<=.f64 v #s(literal 4457913959828945/151115727451828646838272 binary64)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (sin.f64 v) e))) |
(if (<=.f64 v #s(literal 4457913959828945/151115727451828646838272 binary64)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 #s(literal 1 binary64) e)) v)) #s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 e (sin.f64 v)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 e #s(literal 1 binary64))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 (/.f64 e (+.f64 #s(literal 1 binary64) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (fma.f64 v e (*.f64 (*.f64 (neg.f64 e) v) e)))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ (- 0 (* (/ e (- -1 e)) (/ e (- -1 e)))) (+ 0 (/ e (- -1 e)))) (-.f64 e (*.f64 e e))) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) (*.f64 #s(approx (/ e (+ e 1)) (*.f64 (-.f64 #s(literal 1 binary64) e) e)) v)) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 v e)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (-.f64 v (*.f64 e v)) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) e) v) e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 v e))) |
#s(approx (/ (* e (sin v)) (+ 1 (* e (cos v)))) #s(approx (* (/ e (+ e 1)) v) (*.f64 e v))) |
| 15 582× | lower-fma.f64 |
| 15 582× | lower-fma.f32 |
| 14 148× | lower-fma.f64 |
| 14 148× | lower-fma.f32 |
| 8 236× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 463 | 5965 |
| 1 | 1475 | 5741 |
| 2 | 4643 | 5653 |
| 0 | 8163 | 5331 |
| 0 | 583 | 7025 |
| 1 | 1899 | 6814 |
| 2 | 5718 | 6703 |
| 0 | 8332 | 6334 |
| 0 | 35 | 191 |
| 0 | 56 | 191 |
| 1 | 221 | 191 |
| 2 | 1484 | 183 |
| 0 | 8832 | 174 |
| 0 | 182 | 1153 |
| 1 | 554 | 1138 |
| 2 | 1582 | 1106 |
| 3 | 5266 | 1024 |
| 0 | 8387 | 956 |
| 0 | 46 | 285 |
| 0 | 72 | 285 |
| 1 | 262 | 279 |
| 2 | 1645 | 275 |
| 0 | 8579 | 267 |
| 0 | 9 | 27 |
| 0 | 15 | 27 |
| 1 | 42 | 27 |
| 2 | 241 | 27 |
| 3 | 2097 | 27 |
| 0 | 8370 | 25 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 282 to 191 computations (32.3% saved)
(negabs v)
Compiled 538 to 330 computations (38.7% saved)
Loading profile data...